Technical notes on a theory of simplicity
- 38 Downloads
Recently Samuel Richmond, generalizing Nelson Goodman, has proposed a measure of the simplicity of a theory that takes into account not only the polymorphicity of its models but also their internal homogeneity. By this measure a theory is simple if small subsets of its models exhibit only a few distinct (i.e., non-isomorphic) structures. Richmond shows that his measure, unlike that given by Goodman's theory of simplicity of predicates, orders the order relations in an intuitively satisfactory manner. In this note I formalize his presentation and suggest an improvement designed to overcome certain technical difficulties.
KeywordsSmall Subset Technical Difficulty Order Relation Satisfactory Manner Internal Homogeneity
Unable to display preview. Download preview PDF.
- Chang, C. C., and Keisler, H. J.: 1973, Model Theory, American Elsevier Publishing Company, Inc., NY.Google Scholar
- Goodman, N.: 1961, ‘Safety, Strength, and Simplicity’, Philosophy of Science 28, 150–1. Reprinted in 1972, Problems and Projects, pp. 334–336.Google Scholar
- Goodman, N.: 1977, The Structure of Appearance, 3rd edition, D. Reidel, Boston.Google Scholar
- Goodman, N.: 1983, Fact, Finction, and Forecast, Harvard University Press, Cambridge, MA.Google Scholar
- Harary, F.: 1969, Graph Theory, Addison-Wesley Publishing Co., Reading, MA.Google Scholar
- Richmond, Samuel A.: 1996, ‘A Simplification of the Theory of Simplicity’, Synthese 107, 373–393.Google Scholar