• Korean Journal of Cognitive Science
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• v.23 no.3
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• pp.367-388
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• 2012

The centennial of Alan Mathison Turing(23 June 1912 - 7 June 1954) is an appropriate occasion on which to assess his profound influence on the development of cognitive science. His contributions to and attitudes toward that field are discussed from the metamathematical perspective. This essay addresses (i)Turing's mathematical analysis of cognition, (ii)universal Turing machines, (iii)the limitations of universal Turing machines, (iv)oracle Turing machine beyond universal Turing machine, and (v)Turing test for cognitive science. Turing was a ground-breaker, eager to move on to new fields. He actually opened wider the scientific windows to the mind. The results show that first, by means of mathematical logic Turing discovered a new bridge between the mind and the physical world. Second, Turing gave a new formal analysis of operations of the mind. Third, Turing investigated oracle Turing machines and connectionist network machines as new models of minds beyond the limitations of his own universal machines. This paper explores why the cognitive scientist would be ever expecting a new Turing Test on the shoulder of Alan Turing.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.27-36
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• 2004

This paper addresses G$\ddot{o}$del's critique of Turing's mechanism that a configuration of the Turing machine corresponds to each state of human mind. The first part gives a quick overview of Turing's analysis of cognition as computation and its variants. In the following part, we describe the concept of Turing machines, and the third part explains the computational limitations of Turing machines as a cognitive system. The fourth part demonstrates that Godel did not agree with Turing's argument, sometimes referred to as mechanism. Finally, we discuss an oracle Turing machine and its implications.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.31-44
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• 2009

Anyone wishing to understand cognitive science, a converging science, need to become familiar with three major mathematical landmarks: Turing machines, Neural networks, and $G\ddot{o}del's$ incompleteness theorems. The present paper aims to explore the mathematical foundations of cognitive science, focusing especially on these historical landmarks. We begin by considering cognitive science as a metamathematics. The following parts addresses two mathematical models for cognitive systems; Turing machines as the computer system and Neural networks as the brain system. The last part investigates $G\ddot{o}del's$ achievements in cognitive science and its implications for the future of cognitive science.

• Korean Journal of Cognitive Science
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• v.6 no.3
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• pp.5-23
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• 1995

According to a well-known argument (so-called the Godelian argument) proposed by Lucas. Godel's theorem refutes the thesis of mechanism. that is, the thesis that human cognitive system is no more than a Turing machine. The main aim of this paper is to show that this argument is not successful. However. I also argue that many pre-existing objections (by Benacerraf, Slezak. Boyer. Hofstadter etc.) to Gooelian argument are not satisfactory. either. Using Tarski's theorem. I then strengthen what I caII the consistency objection to Godelian argument. In my dilemma objection obtained. Godelian argument doesn't work because the argument has a false premise if we have the concept of global truth and the argument cannot be stated if not.

• Korean Journal of Cognitive Science
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• v.8 no.1
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• pp.37-56
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• 1997

Can the appropriately programmed computer think?I analyse,in this paper, argugments for and against strong AI-thesis,basically Turing's argument and Searle's chinese room argument.Through a cirtical review of these arguments, I try to show that the supportes of Al-thesis like Turing fail to explain the subjective nature of human consciousness.However,I do not think that subjective consciousness is a necessary condition for the ability to understand language.(In this respect my views are different from Searle's). But when we consider the conditions of humans as language users,we should presuppose that a human being is the unity of body and mind (or consciousness). Therefore, our subjective consciousness,together with human body(thus,way of our behavior and life). serve as a mark of person.