David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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International Studies in the Philosophy of Science 11 (1):7 – 20 (1997)
It is argued, by use of specific examples, that mathematical understanding is something which cannot be modelled in terms of entirely computational procedures. Our conception of a natural number (a non-negative integer: 0, 1, 2, 3,…) is something which goes beyond any formulation in terms of computational rules. Our ability to perceive the properties of natural numbers depends upon our awareness, and represents just one of the many ways in which awareness provides an essential ingredient to our ability to understand. There is no bar to the quality of understanding being the result of natural selection, but only so long as the physical laws contain a non-computational ingredient.
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References found in this work BETA
David J. Chalmers (1996). The Conscious Mind: In Search of a Fundamental Theory. Oxford University Press.
Stephen Cole Kleene (1952). Introduction to Metamathematics. North Holland.
John R. Lucas (1961). Minds, Machines and Godel. Philosophy 36 (April-July):112-127.
Roger Penrose (1996). Beyond the Doubting of a Shadow. Psyche 2:89-129.
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