New Directions for Neo-logicism

Thomas-Bolduc, Aaron Robert

New Directions for Neo-logicism

dc.contributor.advisor	Zach, Richard
dc.contributor.author	Thomas-Bolduc, Aaron Robert
dc.contributor.committeemember	Wyatt, Nicole
dc.contributor.committeemember	Liebesman, David
dc.date	2018-11
dc.date.accessioned	2018-07-11T21:05:14Z
dc.date.available	2018-07-11T21:05:14Z
dc.date.issued	2018-07-10
dc.description.abstract	In this dissertation I focus on a program in the philosophy of mathematics known as neo-logicism that is a direct descendant of Frege’s logicist project. That program seeks to reduce mathematical theories to logic and definitions in order to put those theories on stable epistemic and logical footing. The definitions that are of greatest importance are abstraction principles, biconditionals associating identity statements for abstract objects on one side, with equivalence classes on the other. Abstraction principles are important because they provide connections between logic on the one hand, and mathematics and its ontology on the other. Throughout this work, I advocate that the epistemic goals of neo-logicism be taken into account when we’re looking to solve problems that are of central importance to its success. Additionally, each chapter either discusses or advocates for a methodological shift, or sets up and implements a novel methodological position I believe to be broadly beneficial to the neo-logicist project. Chapter 2 traces thinking about the status of higher-order logic through the mid-twentieth century, setting the stage for issues dealt with in later chapters. Chapter 3 asks neo-logicists to look beyond set theory and consider other foundational theories, or something entirely new when looking for reductions of foundational mathematical theories. Chapter 4 is an extended argument involving non-standard analysis showing that Hume’s Principle ought not be considered analytic in Frege’s sense of the termChapters 5 and 6 move away form the (somewhat) historical work in the first three chapters, and set up new strategies for solving central neo-logicist problems by integrating formal and epistemic considerations. Chapter 5 introduces the notion of a canonical equivalence relation via a discussion of content carving. That notion is a particular way of understanding the relationship between equivalence relations and abstracts. Finally, chapter 6 makes use of canonical equivalence relations to introduce a new direction in the search for solutions to the Bad Company objection. As whole, the project can be seen as providing, as the title suggests, new directions that ought to be considered by those wishing to vindicate neo-logicism	en_US
dc.identifier.citation	Thomas-Bolduc, A. R. (2018). New Directions for Neo-logicism (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/32353	en_US
dc.identifier.doi	http://dx.doi.org/10.11575/PRISM/32353
dc.identifier.uri	http://hdl.handle.net/1880/107131
dc.language.iso	eng
dc.publisher.faculty	Arts
dc.publisher.faculty	Graduate Studies
dc.publisher.institution	University of Calgary	en
dc.publisher.place	Calgary	en
dc.rights	University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subject	Logicism
dc.subject	Neo-logicism
dc.subject	Logic
dc.subject	Bad Company
dc.subject	Philosophy of Mathematics
dc.subject.classification	Philosophy	en_US
dc.title	New Directions for Neo-logicism
dc.type	doctoral thesis
thesis.degree.discipline	Philosophy
thesis.degree.grantor	University of Calgary
thesis.degree.name	Doctor of Philosophy (PhD)
ucalgary.item.requestcopy	true