Minds, Machines and Gödel is the title of a philosophical paper published in 1961 by J. R. Lucas.
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.
Lucas 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. Other philosophers, notably Roger Penrose, have made similar arguments.
