# Browsing by Subject "logic"

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Item Bayesians Can Learn From Old Data(2007-11) Jefferys, W. H.; Jefferys, William H.Show more In a widely-cited paper, Glymour (Theory and Evidence, Princeton, N. J.: Princeton University Press, 1980, pp. 63-93) claims to show that Bayesians cannot team from old data. His argument contains an elementary error. I explain exactly where Glymour went wrong, and how the problem should be handled correctly. When the problem is fixed, it is seen that Bayesians, just like logicians, can indeed learn from old data.Show more Item Cartesian Closed Categories and Typed Lambda Calculi(2016) Menezes, Dean; Blumberg, AndrewShow more Typed lambda categories and Cartesian closed categories are both means of formalizing the process of substitution; we demonstrate that these views are essentially the same; specifically that there is an equivalence between the category of small Cartesian closed categories and the category of typed lambda calculi. First we introduce the basic notions of category, functor, monad, comonad and equivalence of categories; then we use these notions to define the category of small Cartesian closed categories and describe how additional arrows may be adjoined to a Cartesian closed category. Next we provide a definition of a typed lambda calculus and describe the structure-preserving maps or translations between typed lambda calculi. Next we provide a definition of a typed lambda calculus and describe the structure-preserving maps or translations between typed lambda calculi. Having defined the two categories we provide descriptions of functors L : Cart_N to lambda-calc and C: lambda-calc to Cart_N and then show that the functors give an equivalence of categories.Show more Item “When almost everything you thought you knew is wrong”: The Science and Mathematics of Tom Stoppard’s plays(2023) Cacciatore, VincentShow more Over his career of more than half a century, playwright Tom Stoppard has built a reputation for using scientific and mathematical concepts in his cerebral plays. Despite this being a well-recognized part of his writing, it is neither a well-studied nor universally liked part of his writing. Two of his most scientific plays (Hapgood and The Hard Problem), for instance, are often not well received by critics. Furthermore, it can be easy to dismiss Stoppard’s use of science and math as just throwaway gags or extra padding to make his plays seem more intellectual. This thesis aims to rebut these attitudes towards Stoppard’s use of science and math by showing their deliberateness and cleverness. This thesis aims to show both Stoppard’s skill in explaining the math and science he uses as well as how the math and science is intentionally used to communicate the themes in many of his plays regardless of subject matter. When one starts to study Stoppard’s use of science and math, they also see Stoppard shift his stance towards science and math between plays. This thesis will thus be framed as an exploration of Stoppard’s dialogue on science and math’s intersection with the humanities. This thesis takes two plays from three different parts of Stoppard’s career: Rosencrantz and Guildenstern Are Dead and Jumpers from Stoppard’s early career; Hapgood and Arcadia from the middle of his career; The Hard Problem and Leopoldstadt from his late career. Through these plays we see Stoppard waver between being skeptical of and embracing math and science. This thesis thus also aims to provide insight on Stoppard’s growth and change as a writer over time.Show more