Abstract
This dissertation investigates the epistemology of three meta-theoretic properties of mathematical theories: consistency, soundness and categoricity. These properties are essential for the integrity and significance of (many) inquiries into mathematical subject matters and are of great importance in the philosophy of mathematics.Although these meta-theoretic properties have been extensively investigated in mathematical and philosophical logic, they have received little of their well-deserved attention in the epistemology of mathematics. This dissertation aims to make some progress concerning some important epistemological issues about these metatheoretic properties.
This thesis is divided into three parts: Part I focuses on the epistemology of consistency, investigating issues concerning belief and knowledge of consistency statements. Part II investigates the role of soundness statements for the coherence of mathematical inquiries. Finally, Part III provides an investigation of categoricity.
| Date of Award | 27 Sept 2022 |
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| Original language | English |
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| Supervisor | Catrin Campbell-Moore (Supervisor) & Johannes Stern (Supervisor) |