Philosophical accounts of reduction between two scientific theories have tended to focus on the relationships between the laws of the two theories, but the current received view of scientific theories considers them to be characterized instead by their collection of models, i.e. the solutions to those laws. The main goal of the proposed project is to develop a class of methodological tools from topology that will close the gap between formal accounts of reduction and scientific theories, advancing both the debate on intertheoretic reduction in philosophy of science and applying fruitfully and immediately to many pairs of physical theories, such as general relativity and Newtonian gravitation. This is helpful for physicists, who are interested, for example, in determining under what circumstances one can approximate or idealize a physical system of interest modeled in a complex theory by one in a simpler theory. It also clarifies the nature of correspondence limits between theories, which continue to be useful guides to the construction of new theories (e.g. of quantum gravity). These limits in turn will yield a storehouse of data with which to test philosophical accounts of reduction.
Although much of the mathematics of these tools has been available for some time, they have received little attention in the physics and philosophy of science literatures. This is perhaps because they had not until recently received a satisfactory interpretation, which I have developed in my doctoral dissertation. Accordingly, few others have a knowledge base overlapping the appropriate mathematics, physics, and philosophy of science to transfer these new techniques successfully to my proposed host.
Fields of science
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