Turing machine - A simple mechanical device consisting solely of a tape, a read/write head, and a finite state machine. Turing was able to show that this machine is able to perform all the operations a person working with a logical system would be able to perform.
The Turing machine has had a central role in theories of computation and computability since the mid 1930s when they were introduced as a rigorous means of defining the concept of 'method' (or algorithm) by Alan Turing. The machine itself is quite simple: it consists solely of a tape, a read/write head and a table of state changes. The tape is divided into discrete boxes, each of which may have either a zero or a one in it. The head will read or write a zero or one, depending on the current state and what is in the current tape-square which the head reads. Despite the simplicity of this idea, it lays all the foundations for understanding the modern computer and computation in general.
Turing was able to show that the Turing machine was a mechanical process that was able to perform all the operations a person working with a logical system would be able to perform. Alonzo Church, in reference to Turing's work, formulated what is now referred to as the Church-Turing thesis; namely, that all definitions of computability are equivalent (i.e. Turing machine computable functions are all the computable functions there are). In other words, Turing machines can compute any function that is computable, assuming that both the tape and time are infinite.
With the further premise that people are, in a theoretical sense, computers, it is a natural conclusion that our behavior can be captured in the language of the Turing machine (see functionalism). Indeed, Turing himself argued that the Turing machine was equivalent to what could be achieved by the human brain, assuming a finite number of possible brain states (Hodges 1995). There are two obvious assumptions of this position. First there is the assumption that we are computational. Second, is the assumption that we have a finite number of brain states. However, it is the more subtle notion of 'equivalence' which is most problematic. It can be claimed that it is a misunderstanding of what Turing machine equivalence is, and how it is related to implementation, that has misled many philosophers of mind to simply transport conclusions about Turing machines to the realm of human psychology.
In particular, Turing machine equivalence has been used to support the claim that the goal of psychology is to provide a purely functional, implementation independent, description of human behavior. In general, the reasoning goes as follows.
Clearly, Turing Machine states are fully definable in terms of inputs, outputs, and machine states. We need not have any commitments to the physical realization of the machine, as it is the state transitions that count in the case of the Turing machine. In fact, to completely explain a Turing machine state we need only specify three things: 1) the machine's input; 2) the output of the machine given its state and that input; and 3) the next state of the machine given the current state. All that matters to what a state is, is what the machine does – thus Turing machine states are functionally defined.
Given this fact, and the fact that human beings can be described in Turing machine terms, it is not surprising that the view that we, ourselves, should be functionally understood naturally follows. For obvious reasons, this philosophical position became known as functionalism. Functionalism, in its various forms, is espoused by many contemporary philosophers; particularly those interested in mind and the sciences.
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