Underdetermination, Multiplicity, and Mathematical Logic

Whether a collection of scientific data can be explained only by a unique theory or whether such data can be equally explained by multiple theories is one of the more contested issues in the history and philosophy of science. This paper argues that the case for multiple explanations is strengthened by the widespread failure of models in mathematical logic to be unique, i.e., categorical. Science is taken to require replicable and explicit public knowledge; this necessitates an unambiguous language for its transmission. Mathematics has been chosen as the vehicle to transmit scientific knowledge, both because of its ＂unreasonable effectiveness＂ and because of its unambiguous nature, hence the vogue of axiomatic systems. But mathematical logic tells us that axiomatic systems need not refer to uniquely defined real structures. Hence what is accepted as science may be only one of several possibilities.