Minds, Machines and Gödel
Encyclopedia
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 over mechanism.
Lucas presented the paper in 1959 to the Oxford Philosophical Society. 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 0135833930.
John Lucas (philosopher)
- Overview :John Lucas was educated at Winchester College and Balliol College, Oxford, where he studied first mathematics, then Greats , obtaining first class honors, and proceeding to an MA in Philosophy in 1954. He spent the 1957-58 academic year at Princeton University, deepening his...
's 1959 philosophical paper in which he argues that a human mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
cannot be accurately represented by an algorithmic automaton
Turing machine
A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...
. 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 over mechanism.
Lucas presented the paper in 1959 to the Oxford Philosophical Society. 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 0135833930.