No Provable Limits to ‘Scientific Knowledge’

In an article concerning problems that are impossible to solve exactly, but which can be computed in an average sense, J. F. Traub and H. Wozniakowski raised a challenge: “We believe it is time to up the ante and try to prove there are unanswerable scientific questions. In other words, we would like to establish a physical Gödel’s theorem.” Out of this idea grew a workshop at the Santa Fe Institute (May 24-26, 1994), chaired by John Casti and J. F. Traub, entitled “Limits to Scientific Knowledge.” This workshop involved biologists, physicists, economists, philosophers, psychologists, mathematicians, and computer scientists, all with various visions of “limitations,” involving the natural sciences or otherwise. Some of the ruminations of this group, and their subsequent e-mail exchanges, have been collected in a Santa Fe Institute Report. The title of this report, “On Limits,” omits reference to “scientific knowledge,” which was largely unaddressed at this workshop. Likewise, published commentaries in the media concerning this workshop did not take notice of this basic concept. In this article one concept of ‘scientific knowledge’ will be outlined, and the issue of limits of this scientific knowledge will be addressed.