GoKawiilFirst published Fri Oct 16, 2015; substantive revision Wed Dec 18, 2024
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:
There are infinitely many memory locations, arrayed in a linear structure. Metaphorically, these memory locations are “cells” on an infinitely long “paper tape”. More literally, the memory locations might be physically realized in various media (e.g., silicon chips).
There is a central processor, which can access one memory location at a time. Metaphorically, the central processor is a “scanner” that moves along the paper tape one “cell” at a time.
The central processor can enter into finitely many machine states.
The central processor can perform four elementary operations: write a symbol at a memory location; erase a symbol from a memory location; access the next memory location in the linear array (“move to the right on the tape”); access the previous memory location in the linear array (“move to the left on the tape”).
Which elementary operation the central processor performs depends entirely upon two facts: which symbol is currently inscribed at the present memory location; and the scanner’s own current machine state.
A machine table dictates which elementary operation the central processor performs, given its current machine state and the symbol it is currently accessing. The machine table also dictates how the central processor’s machine state changes given those same factors. Thus, the machine table enshrines a finite set of routine mechanical instructions governing computation.
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