Topics in arithmetic and determinacy
<p>This thesis is about Arithmetical Determinacy. Loosely, this is the problem of whether every question in arithmetic has a determinate answer. In this work I discuss how to exactly understand the concept of determinacy, I criticise arguments for and against the claim that arithmetic is deter...
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| Format: | Thesis |
| Language: | English |
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2023
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| Summary: | <p>This thesis is about Arithmetical Determinacy. Loosely, this is the problem of whether every question in arithmetic has a determinate answer. In this work I discuss how to exactly understand the concept of determinacy, I criticise arguments for and against the claim that arithmetic is determinate, and examine how questions about determinacy may be applied to other debates in the philosophy of mathematics.</p>
<p>Chapter 1 isolates different ways of understanding the problem of arithmetical determinacy. Chapter 2 turns to mathematical structuralism and explains how popular computability constraints thought to determine the reference of our arithmetical vocabulary are actually unsuccessful in securing determinacy. Chapter 3 criticises an interesting idea for securing determinacy via our experience with supertasks. Chapter 4 explores the phenomenon of mutually inconsistent satisfaction classes and motivates a new account of determinacy in terms of sentences possessing non-classical truth-values. Chapter 5 defends strict finitism, framing some objections against the view in terms of the concept of arithmetical determinacy.</p> |
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