Boaz D Laan

In contemporary philosophical discourse modality plays a central theoretical role. One approach to formalising modalities is what this thesis calls the mention predicate approach, where a modality is formalised as a first-order predicate that predicates on names of sentences / formulae, or names of propositions. There is a relative lack of philosophical interest in the mention predicate approach because it is prone to paradox, most notably Montague’s Paradox. This thesis argues why this is unwarranted; and critically assesses and contributes to topics relating to the mention predicate approach. Chapter 3 of this thesis critically assesses how Stern 2014c; Stern 2015 resolves the paradoxes of the mention predicate approach. Chapter 4 of this thesis contributes to the categorisation of the paradoxes that the mention predicate approach is prone to. Moreover, this chapter contributes to the understanding of the extent and limitations of the semantics of the mention predicate approach. In particular, chapter 4 provides a limitative result which functions as a categorisation theorem indicating when paradox arises. Chapter 5 of this thesis provides an example of a modality in the philosophical literature that is most appropriately formalised using the mention predicate approach. In particular, chapter 5 critically assesses the account of modal potentialism in the philosophy of mathematics developed by Linnebo 2018. In doing so, chapter 5 shows that, as it stands, Linnebo 2018 provides an account of modal potentialism that is incoherent.

Modal potentialism argues that mathematics has a generative nature, and aims to formalise mathematics accordingly using quantified modal logic. This paper shows that Øystein Linnebo’s approach to modal potentialism in his book Thin Objects is incoherent. In particular, he is committed to the legitimacy of introducing a primitive modal predicate of formulae. However, as with the semantic paradoxes, natural principles for such a predicate are inconsistent; no such predicate can underpin an account of modal potentialism. Hence, Linnebo’s intended interpretation of the primitive modality and his formal framework do not match up.