Doctor of Philosophy, The Ohio State University, 2019, Philosophy

Ordinary kinds, K, admit of leeway, both in the number of things that must be arranged K-wise and even in what arrangements count as being arranged K-wise. Consider a chair. A slightly smaller collection of things in pretty much the same arrangement would presumably still be some things arranged chairwise and would count as a chair. But there are plausibly many such collections of things in the vicinity of any chair. Thus, it seems that I am seated in many chairs. This is an instance of the problem of the many. The first half of the dissertation is about solutions to the problem of the many. In chapter 2, I evaluate the proposal that constitution, a relation of non-identity between a thing and what it is made out of, is needed to solve the problem. I argue against this by showing that parallel, constitution-free solutions solve the problem using the very same machinery as constitutionalists, sans constitution. In chapter 3, I develop, motivate, and defend a novel solution to the problem of the many. According to this solution, the many things that have what it takes to be a chair, say, are collectively identical to a single chair. In the second half of the dissertation, I discuss problems of the many that arise in personal ontology. The thinking animal problem is the main argument for animalism, the thesis that human persons are identical to animals. Animalists use this problem against constitutionalism, the thesis that human persons are constituted by, but not identical to, human animals. The thinking animal problem challenges constitutionalists to avoid the result that both the person and animal think. Animalists face the thinking parts problem, which challenges them to avoid the result that the human animal and its large proper parts think. In chapter 4, I argue that constitutionalists about human persons can solve the thinking animal problem using solutions parallel to those animalists use to solve the thinking parts problem. Furthermore, I argue that ani (open full item for complete abstract)

Committee: Benjamin Caplan (Committee Co-Chair); Julia Jorati (Committee Co-Chair); Taschek William (Committee Member) Subjects: Philosophy

Doctor of Philosophy, The Ohio State University, 2018, Physics

Low-energy nuclear physics has seen a renaissance of activity recently with the advent of the nuclear effective field theory (EFT) approach, the power of renormalization group techniques, and advances in the computational cost-effectiveness and sophistication of quantum many-body methods. Nevertheless challenges remain in part from ambiguities of the nuclear Hamiltonian via regulator artifacts and the scaling of the many-body methods to heavier systems. Regulator artifacts arise due to a renormalization inconsistency in the nuclear EFT as currently formulated in Weinberg power counting, though their ultimate impact on nuclear observables is unknown at present. This results in a residual cutoff dependence in the EFT to all orders. We undertake an examination of these regulator artifacts using perturbative energy calculations of uniform matter as a testbed. Our methodology has found that the choice of regulator determines the shape of the energy phase space and that different regulators weight distinct phase space regions differently. Concerning many-body calculations, at present only phenomenological energy density functionals are able to solve for the full table of nuclides. However these functionals are currently unconnected to QCD and have no existing method for systematic improvement. A technique, the density matrix expansion (DME), is one way to add microscopic chiral physics into these energy functionals. We develop a new formulation of the DME using local coordinate space regulators and allow for explicit Delta isobars in the chiral potentials. The resulting functionals show systematic improvement order-by-order in the chiral expansion and have non-trivial improvements in nuclear binding energy residuals over the previous Skyrme state of the art. Furthermore, renormalization group methods have also proved quite successful at taming certain nonperturbative aspects of nuclear potentials. However at present a robust many-body power counting scheme for (open full item for complete abstract)

Committee: Richard Furnstahl (Advisor); Robert Perry (Committee Member); Michael Lisa (Committee Member); Junko Shigemitsu (Committee Member) Subjects: Nuclear Physics; Physics

Doctor of Philosophy, The Ohio State University, 1979, Graduate School

Committee: Not Provided (Other) Subjects: Mathematics