Montague's Paradox without Necessitation

TL;DR

This paper demonstrates that Montague's paradox can be derived without relying on the necessitation rule, challenging previous claims that necessitation is essential for the paradox.

Contribution

It provides a derivation of Montague's paradox in modal system T without necessitation, showing the paradox's independence from that rule.

Findings

Montague's paradox can be derived without necessitation.

A weaker modal system also supports the derivation.

The paradox's core does not depend on the necessitation rule.

Abstract

Some such as Dean (2014) suggest that Montague's paradox requires the necessitation rule, and that the use of the rule in such a context is contentious. But here, I show that the paradox arises independently of the necessitation rule. A derivation of the paradox is given in modal system T without deploying necessitation; a necessitation-free derivation is also formulated in a significantly weaker system.