Proof and Prejudice: Why Formalising Doesn’t Make You a Formalist

The topic of this thesis is the relationship between formal and informal proofs. Chapter One opens the discussion by examining what a proof is, when two proofs are identical, what the purpose of proving is and how to distinguish the two categories of proof. Chapters Two and Three focus in on informal and formal proof respectively, with the latter also including descriptions of various computational proof checkers and the Formalist family of positions in the Philosophy of Mathematics. In Chapter Four I look at the Formalisability Thesis, that every informal proof corresponds to a formal proof, and argue that this breaks apart into a weak and a strong reading. In Chapter Five, I outline a simple mathematical problem and attempt the practical process of formalisation, following which I consider the decisions that were involved in doing so. Finally, in Chapter Six, I use what was learned from the practicalities of formalisation to argue in favour of the weak reading of the Formalisability Thesis, which I take to be closely related to Carnapian explication, but against the strong reading, which corresponds to the Formalists’ approach to formalisation.