Article URL: https://plato.stanford.edu/entries/computational-mind/ Comments URL: https://news.ycombinator.com/item?id=49149125 Points: 23 # Comments: 8

Could a machine think? Could the mind itself be a thinking machine? The computer revolution transformed discussion of these questions, offering our best prospects yet for machines that emulate reasoning, decision-making, problem solving, perception, linguistic comprehension, and other mental processes. Advances in computing raise the prospect that the mind itself is a computational system—a position known as the computational theory of mind (CTM). Computationalists are researchers who endorse CTM, at least as applied to certain important mental processes. CTM played a central role within cognitive science during the 1960s and 1970s. For many years, it enjoyed orthodox status. More recently, it has come under pressure from various rival paradigms. A key task facing computationalists is to explain what one means when one says that the mind “computes”. A second task is to argue that the mind “computes” in the relevant sense. A third task is to elucidate how computational description relates to other common types of description, especially neurophysiological description (which cites neurophysiological properties of the organism’s brain or body) and intentional description (which cites representational properties of mental states). The intuitive notions of computation and algorithm are central to mathematics. Roughly speaking, an algorithm is an explicit, step-by-step procedure for answering some question or solving some problem. An algorithm provides routine mechanical instructions dictating how to proceed at each step. Obeying the instructions requires no special ingenuity or creativity. For example, the familiar grade-school algorithms describe how to compute addition, multiplication, and division. Until the early twentieth century, mathematicians relied upon informal notions of computation and algorithm without attempting anything like a formal analysis. Developments in the foundations of mathematics eventually impelled logicians to pursue a more systematic treatment. Alan Turing’s landmark paper “On Computable Numbers, With an Application to the Entscheidungsproblem” (Turing 1936) offered the analysis that has proved most influential. A Turing machine is an abstract model of an idealized computing device with unlimited time and storage space at its disposal. The device manipulates symbols, much as a human computing agent manipulates pencil marks on paper during arithmetical computation. Turing says very little about the nature of symbols. He assumes that primitive symbols are drawn from a finite alphabet. He also assumes that symbols can be inscribed or erased at “memory locations”. Turing’s model works as follows: Turing translates this informal description into a rigorous mathematical model. For more details, see the entry on Turing machines. Turing motivates his approach by reflecting on idealized human computing agents. Citing finitary limits on our perceptual and cognitive apparatus, he argues that any symbolic algorithm executed by a human can be replicated by a suitable Turing machine. He concludes that the Turing machine formalism, despite its extreme simplicity, is powerful enough to capture all humanly executable mechanical procedures over symbolic configurations. Subsequent discussants have almost universally agreed. Turing computation is often described as digital rather than analog. What this means is not always so clear, but the basic idea is usually that computation operates over discrete configurations. By comparison, many historically important algorithms operate over continuously variable configurations. For example, Euclidean geometry assigns a large role to ruler-and-compass constructions, which manipulate geometric shapes. For any shape, one can find another that differs to an arbitrarily small extent. Symbolic configurations manipulated by a Turing machine do not differ to arbitrarily small extent. Turing machines operate over discrete strings of elements (digits) drawn from a finite alphabet. One recurring controversy concerns whether the digital paradigm is well-suited to model mental activity or whether an analog paradigm would instead be more fitting (MacLennan 2012; Piccinini and Bahar 2013).[1] Besides introducing Turing machines, Turing (1936) proved several seminal mathematical results involving them. In particular, he proved the existence of a universal Turing machine (UTM). Roughly speaking, a UTM is a Turing machine that can mimic any other Turing machine. One provides the UTM with a symbolic input that codes the machine table for Turing machine M. The UTM replicates M’s behavior, executing instructions enshrined by M’s machine table. In that sense, the UTM is a programmable general purpose computer. To a first approximation, all personal computers are also general purpose: they can mimic any Turing machine, when suitably programmed. The main caveat is that physical computers have finite memory, whereas a Turing machine has unlimited memory. More accurately, then, a personal computer can mimic any Turing machine until it exhausts its limited memory supply. Turing’s discussion helped lay the foundations for computer science, which seeks to design, build, and understand computing systems. As we know, computer scientists can now build extremely sophisticated computing machines. All these machines implement something resembling Turing computation, although the details differ from Turing’s simplified model.