In ‘A New Conditional for Naive Truth Theory’, Andrew Bacon provides a fixed-point construction for a conditional in a self-referential framework. His proof makes use of the Banach fixed point theorem, but we show that its result is equivalent to a simple strict conditional in a converse well-founded frame. We give a general construction for finding fixed points based on converse well-founded structures. In fact, many fixed point accounts can be seen as instances of this general setting.
In further work, we will show how many different accounts can be subsumed under this approach (Brady, Field), and show the connection to provability logic.