It is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest. A structural representation depends on the existence of a common structure between a representation and that which it represents, and it is important because it allows us to reason directly about the representation in order to draw conclusions about the (...) phenomenon that it depicts. The present goal is to give a general and precise account of structural representation, then to use that account to illuminate several problems of current philosophical interest — including some that do not initially seem to involve representation at all. In particular, it is argued that ontological reductions (like that of the natural numbers to sets), compositional accounts of semantics, several important sorts of mental representation, and (perhaps) possible worlds semantics for intensional logics are all species of structural representation and are fruitfully studied in the framework developed here. (shrink)

I examine one of the conceptual cornerstones of the field known as computational neuroscience, especially as articulated in Churchland et al. (1990), an article that is arguably the locus classicus of this term and its meaning. The authors of that article try, but I claim ultimately fail, to mark off the enterprise of computational neuroscience as an interdisciplinary approach to understanding the cognitive, information-processing functions of the brain. The failure is a result of the fact that the authors provide no (...) principled means to distinguish the study of neural systems as genuinely computational/information-processing from the study of any complex causal process. I then argue for two things. First, that in order to appropriately mark off computational neuroscience, one must be able to assign a semantics to the states over which an attempt to provide a computational explanation is made. Second, I show that neither of the two most popular ways of trying to effect such content assignation -- informational semantics and 'biosemantics' -- can make the required distinction, at least not in a way that a computational neuroscientist should be happy about. The moral of the story as I take it is not a negative one to the effect that computational neuroscience is in principle incapable of doing what it wants to do. Rather, it is to point out some work that remains to be done. (shrink)

This paper offers an account of what it is for a physical system to be a computing mechanism—a system that performs computations. A computing mechanism is a mechanism whose function is to generate output strings from input strings and (possibly) internal states, in accordance with a general rule that applies to all relevant strings and depends on the input strings and (possibly) internal states for its application. This account is motivated by reasons endogenous to the philosophy of computing, namely, doing (...) justice to the practices of computer scientists and computability theorists. It is also an application of recent literature on mechanisms, because it assimilates computational explanation to mechanistic explanation. The account can be used to individuate computing mechanisms and the functions they compute and to taxonomize computing mechanisms based on their computing power. (shrink)

The received view is that computational states are individuated at least in part by their semantic properties. I offer an alternative, according to which computational states are individuated by their functional properties. Functional properties are specified by a mechanistic explanation without appealing to any semantic properties. The primary purpose of this paper is to formulate the alternative view of computational individuation, point out that it supports a robust notion of computational explanation, and defend it on the grounds of how computational (...) states are individuated within computability theory and computer science. A secondary purpose is to show that existing arguments for the semantic view are defective. (shrink)

Hilary Putnam has argued that computational functionalism cannot serve as a foundation for the study of the mind, as every ordinary open physical system implements every finite-state automaton. I argue that Putnam's argument fails, but that it points out the need for a better understanding of the bridge between the theory of computation and the theory of physical systems: the relation of implementation. It also raises questions about the class of automata that can serve as a basis for understanding the (...) mind. I develop an account of implementation, linked to an appropriate class of automata, such that the requirement that a system implement a given automaton places a very strong constraint on the system. This clears the way for computation to play a central role in the analysis of mind. (shrink)

This paper explores the difference between Connectionist proposals for cognitive a r c h i t e c t u r e a n d t h e s o r t s o f m o d e l s t hat have traditionally been assum e d i n c o g n i t i v e s c i e n c e . W e c l a i m t h a t t h (...) e m a j o r d i s t i n c t i o n i s t h a t , w h i l e b o t h Connectionist and Classical architectures postulate representational mental states, the latter but not the former are committed to a symbol-level of representation, or to a ‘language of thought’: i.e., to representational states that have combinatorial syntactic and semantic structure. Several arguments for combinatorial structure in mental representations are then reviewed. These include arguments based on the ‘systematicity’ of mental representation: i.e., on the fact that cognitive capacities always exhibit certain symmetries, so that the ability to entertain a given thought implies the ability to entertain thoughts with semantically related contents. We claim that such arguments make a powerful case that mind/brain architecture is not Connectionist at the cognitive level. We then consider the possibility that Connectionism may provide an account of the neural (or ‘abstract neurological’) structures in which Classical cognitive architecture is implemented. We survey a n u m b e r o f t h e s t a n d a r d a r g u m e n t s t h a t h a v e b e e n o f f e r e d i n f a v o r o f Connectionism, and conclude that they are coherent only on this interpretation. (shrink)

On the occasion of a first conference on Cognitive Science, it seems appropriate to review the basis of common understanding between the various disciplines. In my estimate, the most fundamental contribution so far of artificial intelligence and computer science to the joint enterprise of cognitive science has been the notion of a physical symbol system, i.e., the concept of a broad class of systems capable of having and manipulating symbols, yet realizable in the physical universe. The notion of symbol so (...) defined is internal to this concept, so it becomes a hypothesis that this notion of symbols includes the symbols that we humans use every day of our lives. In this paper we attempt systematically, but plainly, to lay out the nature of physical symbol systems. Such a review is in ways familiar, but not thereby useless. Restatement of fundamentals is an important exercise. (shrink)

The paper presents an extended argument for the claim that mental content impacts the computational individuation of a cognitive system (section 2). The argument starts with the observation that a cognitive system may simultaneously implement a variety of different syntactic structures, but that the computational identity of a cognitive system is given by only one of these implemented syntactic structures. It is then asked what are the features that determine which of implemented syntactic structures is the computational structure of the (...) system, and it is contended that these features are certain aspects of mental content. The argument helps (section 3) to reassess the thesis known as computational externalism, namely, the thesis that computational theories of cognition make essential reference to features in the individual's environment. It is suggested that the familiar arguments for computational externalism?which rest on thought experiments and on exegesis of Marr's theories of vision?are unconvincing, but that they can be improved. A reconstruction of the visex/audex thought experiment is offered in section 3.1. An outline of a novel interpretation of Marr's theories of vision is presented in section 3.2. The corrected arguments support the claim that computational theories of cognition are intentional. Computational externalism is still pending, however, upon the thesis that psychological content is extrinsic. (shrink)

Because of the “all-or-none” character of nervous activity, neural events and the relations among them can be treated by means of propositional logic. It is found that the behavior of every net can be described in these terms, with the addition of more complicated logical means for nets containing circles; and that for any logical expression satisfying certain conditions, one can find a net behaving in the fashion it describes. It is shown that many particular choices among possible neurophysiological assumptions (...) are equivalent, in the sense that for every net behaving under one assumption, there exists another net which behaves under the other and gives the same results, although perhaps not in the same time. Various applications of the calculus are discussed. (shrink)

The view that the brain is a sort of computer has functioned as a theoretical guideline both in cognitive science and, more recently, in neuroscience. But since we can view every physical system as a computer, it has been less than clear what this view amounts to. By considering in some detail a seminal study in computational neuroscience, I first suggest that neuroscientists invoke the computational outlook to explain regularities that are formulated in terms of the information content of electrical (...) signals. I then indicate why computational theories have explanatory force with respect to these regularities:in a nutshell, they underscore correspondence relations between formal/mathematical properties of the electrical signals and formal/mathematical properties of the represented objects. I finally link my proposal to the philosophical thesis that content plays an essential role in computational taxonomy. (shrink)

According to Marr, a computational-level theory consists of two elements, the what and the why. This article highlights the distinct role of the Why element in the computational analysis of vision. Three theses are advanced: that the Why element plays an explanatory role in computational-level theories, that its goal is to explain why the computed function is appropriate for a given visual task, and that the explanation consists in showing that the functional relations between the representing cells are similar to (...) the “external” mathematical relations between the entities that these cells represent. (shrink)

I offer an explication of the notion of computer, grounded in the practices of computability theorists and computer scientists. I begin by explaining what distinguishes computers from calculators. Then, I offer a systematic taxonomy of kinds of computer, including hard-wired versus programmable, general-purpose versus special-purpose, analog versus digital, and serial versus parallel, giving explicit criteria for each kind. My account is mechanistic: which class a system belongs in, and which functions are computable by which system, depends on the system's mechanistic (...) properties. Finally, I briefly illustrate how my account sheds light on some issues in the history and philosophy of computing as well as the philosophy of mind. (shrink)

In his 1936 paper,On the Concept of Logical Consequence, Tarski introduced the celebrated definition oflogical consequence: “The sentenceσfollows logicallyfrom the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentenceσ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which (...) follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentenceσis false. Moreover, … we are concerned here with the concept of logical, i.e.,formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since. (shrink)

Computational neuroscientists not only employ computer models and simulations in studying brain functions. They also view the modeled nervous system itself as computing. What does it mean to say that the brain computes? And what is the utility of the ‘brain-as-computer’ assumption in studying brain functions? In previous work, I have argued that a structural conception of computation is not adequate to address these questions. Here I outline an alternative conception of computation, which I call the analog-model. The term ‘analog-model’ (...) does not mean continuous, non-discrete or non-digital. It means that the functional performance of the system simulates mathematical relations in some other system, between what is being represented. The brain-as-computer view is invoked to demonstrate that the internal cellular activity is appropriate for the pertinent information-processing task.Keywords: Computation; Computational neuroscience; Analog computers; Representation; Simulation. (shrink)

In his 1936 paper,On the Concept of Logical Consequence, Tarski introduced the celebrated definition oflogical consequence: “The sentenceσfollows logicallyfrom the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentenceσ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which (...) follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentenceσis false. Moreover, … we are concerned here with the concept of logical, i.e.,formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since. (shrink)

According to Marr, a computational-level theory consists of two elements, the what and the why . This article highlights the distinct role of the Why element in the computational analysis of vision. Three theses are advanced: ( a ) that the Why element plays an explanatory role in computational-level theories, ( b ) that its goal is to explain why the computed function (specified by the What element) is appropriate for a given visual task, and ( c ) that the (...) explanation consists in showing that the functional relations between the representing cells are similar to the “external” mathematical relations between the entities that these cells represent. *Received September 2009; revised January 2010. †To contact the author, please write to: Departments of Philosophy and Cognitive Science, The Hebrew University, Jerusalem 91905, Israel; e-mail: [email protected]. (shrink)