This report is a continuation of (2—5)We introduce several notions such as Skolem functions and sets of indiscernibles, saturated and atomic models, and stable theories in power in lattice-valued version. On the basi...This report is a continuation of (2—5)We introduce several notions such as Skolem functions and sets of indiscernibles, saturated and atomic models, and stable theories in power in lattice-valued version. On the basis of [2—5] Morley categoricity theorem for finite valued lattice is deduced.展开更多
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 ...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.展开更多
文摘This report is a continuation of (2—5)We introduce several notions such as Skolem functions and sets of indiscernibles, saturated and atomic models, and stable theories in power in lattice-valued version. On the basis of [2—5] Morley categoricity theorem for finite valued lattice is deduced.
文摘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.
