A 20th Century Question Anticipated

Newman’s insights provide the basis of an answer to a current question: Is the human mind more capable than a Turing machine in arriving at truth about concrete things that exist? John Henry Newman examined an equivalent question, in which the mind was compared with languages rather than machines. He offered his response in An Essay in Aid of a Grammar of Assent [1870]. Newman anticipated the limitation basic to Gödel's incompleteness result for consistent formal systems, by claiming a fundamental incompleteness property for all languages such as English. He proposed a new definition of "proof" drawn from his own experience of human assent to truth, and based on a mathematical analogy. His analogy suggests that the human mind, in developing a proof, is not confined to finite sequences of words any more than a mathematician or scientist is confined to thinking in terms of rational numbers.

We consider now the implications of Newman’s work for the mind-machine controversy, most recently enlivened by Roger Penrose's contributions in The Emperor's New Mind [1989] and in Shadows of the Mind [1994].