"Minds, Machines and Gödel" is J. R. Lucas's 1959 philosophical paper in which he argues that a human mathematician cannot be accurately represented by an algorithmic automaton. Appealing to Gödel's incompleteness theorem, he argues that for any such automaton, there would be some mathematical formula which it could not prove, but which the human mathematician could both see, and show, to be true. The paper is a Gödelian argument against mechanism.
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| - 마음, 기계 및 괴델 (ko)
- Minds, Machines and Gödel (en)
- Argument van Lucas (nl)
- 心靈、機器與哥德爾 (zh)
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| - 〈마음, 기계 및 괴델〉(Mind, Machines and Gödel)은 J. R. 루카스(Lucas)에 의한 1959년 철학 논문인데 여기서 그는 인간인 수학자를 알고리즘 자동기계로는 정확하게 나타낼 수 없다고 주장하고 있다. 그는 괴델의 불완전성 정리에 기초하여 이러한 자동 기계가 증명할 수는 없지만 인간 수학자는 사실로 인지하여 증명할 수 있는 수학적 공식들이 있을 것으로 주장하고 있다. 이 논문은 기계론(mechanism)에 대한 괴델식 논증이다. 루카스는 이 논문을 1959년 (Oxford Philosophical Society)에 발표했다. 1961년 Philosophy, XXXVI에 처음 발간된 후, The Modeling of Mind, Kenneth M. Sayre and Frederick J. Crosson, eds., Notre Dame Press, 1963 및 Minds and Machines, ed. 앨런 로스 앤더슨, 프렌티스 홀, 1964, ISBN 0-13-583393-0로 재출간되었다. (ko)
- Het argument van Lucas is een filosofisch argument van J.R. Lucas waarbij hij beredeneert dat mensen iets kunnen wat computers niet kunnen, namelijk de waarheid van Gödelzinnen inzien. De redenering is dat computers formele systemen zijn en dat er, volgens de eerste stelling van Gödel, zinnen zijn die binnen een formeel systeem niet bewezen kunnen worden. Een mens kan echter wel de waarheid van zo'n Gödelzin inzien waarmee volgens J.R. Lucas is aangetoond dat de mens iets kan wat computers niet kunnen. (nl)
- 《心靈、機器與哥德爾》（英語：Minds, Machines and Gödel）由於1959年撰寫的哲學論文，他認為人類數學家不能被圖靈機準確替代。本論文以機械論作為哥德爾論證的機制。 受到哥德爾不完備定理的影響，他認為對於任何這樣的自動機，都會有一些它無法證明的數學公式，但是人類數學家可以看到並證明為真。 盧卡斯於1959年將該論文提交給牛津哲學學會。首次出版於《哲學》（Philosophy，XXXVI，1961年），後轉載於《心智模型》與《心靈、機器與哥德爾》。 (zh)
- "Minds, Machines and Gödel" is J. R. Lucas's 1959 philosophical paper in which he argues that a human mathematician cannot be accurately represented by an algorithmic automaton. Appealing to Gödel's incompleteness theorem, he argues that for any such automaton, there would be some mathematical formula which it could not prove, but which the human mathematician could both see, and show, to be true. The paper is a Gödelian argument against mechanism. (en)
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| - "Minds, Machines and Gödel" is J. R. Lucas's 1959 philosophical paper in which he argues that a human mathematician cannot be accurately represented by an algorithmic automaton. Appealing to Gödel's incompleteness theorem, he argues that for any such automaton, there would be some mathematical formula which it could not prove, but which the human mathematician could both see, and show, to be true. The paper is a Gödelian argument against mechanism. Lucas presented the paper in 1959 to the . It was first printed in Philosophy, XXXVI, 1961, then reprinted in The Modeling of Mind, Kenneth M. Sayre and Frederick J. Crosson, eds., Notre Dame Press, 1963, and in Minds and Machines, ed. Alan Ross Anderson, Prentice-Hall, 1964, ISBN 0-13-583393-0. (en)
- 〈마음, 기계 및 괴델〉(Mind, Machines and Gödel)은 J. R. 루카스(Lucas)에 의한 1959년 철학 논문인데 여기서 그는 인간인 수학자를 알고리즘 자동기계로는 정확하게 나타낼 수 없다고 주장하고 있다. 그는 괴델의 불완전성 정리에 기초하여 이러한 자동 기계가 증명할 수는 없지만 인간 수학자는 사실로 인지하여 증명할 수 있는 수학적 공식들이 있을 것으로 주장하고 있다. 이 논문은 기계론(mechanism)에 대한 괴델식 논증이다. 루카스는 이 논문을 1959년 (Oxford Philosophical Society)에 발표했다. 1961년 Philosophy, XXXVI에 처음 발간된 후, The Modeling of Mind, Kenneth M. Sayre and Frederick J. Crosson, eds., Notre Dame Press, 1963 및 Minds and Machines, ed. 앨런 로스 앤더슨, 프렌티스 홀, 1964, ISBN 0-13-583393-0로 재출간되었다. (ko)
- Het argument van Lucas is een filosofisch argument van J.R. Lucas waarbij hij beredeneert dat mensen iets kunnen wat computers niet kunnen, namelijk de waarheid van Gödelzinnen inzien. De redenering is dat computers formele systemen zijn en dat er, volgens de eerste stelling van Gödel, zinnen zijn die binnen een formeel systeem niet bewezen kunnen worden. Een mens kan echter wel de waarheid van zo'n Gödelzin inzien waarmee volgens J.R. Lucas is aangetoond dat de mens iets kan wat computers niet kunnen. (nl)
- 《心靈、機器與哥德爾》（英語：Minds, Machines and Gödel）由於1959年撰寫的哲學論文，他認為人類數學家不能被圖靈機準確替代。本論文以機械論作為哥德爾論證的機制。 受到哥德爾不完備定理的影響，他認為對於任何這樣的自動機，都會有一些它無法證明的數學公式，但是人類數學家可以看到並證明為真。 盧卡斯於1959年將該論文提交給牛津哲學學會。首次出版於《哲學》（Philosophy，XXXVI，1961年），後轉載於《心智模型》與《心靈、機器與哥德爾》。 (zh)
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