The Uses of a Screwdriver Cannot be Listed Algorithmically

A quote from Stuart A. Kauffman, Foreword: Evolution beyond Newton, Darwin, and Entailing Law. In Beyond Mechanism: Putting Life Back Into Biology

p. 9 “Here is the first ‘strange’ step. Can you name all the uses of a screwdriver, alone, or with other objects or process? Well, screw in a a screw, open a paint can, wedge open a door, wedge closed a door, scrape putty off a window, stab an assailant, be an objet d’art, tied to a stick a fish spear, the spear rented to ‘natives’ for a 5 percent fish catch return becomes a new business, and so on. I think that we all are convinced that the following two statements are true: (1) the number of uses of a screw driver is indefinite; and (2) unlike the integers which can be ordered, there is no natural ordering of the uses of a screw driver. The uses are unordered. But these two claims entail that there is no ‘Turing Effective Procedure’ to list all the uses of a screwdriver alone or with other objects or processes. In short, there is no algorithm to list all the uses of a screwdriver.”


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