Dissertation, Birkbeck College, University of London (2014
In philosophical logic,
a certain family of model constructions has received particular attention.
Prominent examples are the cumulative hierarchy of well-founded sets, and Kripke's least fixed point models of grounded truth.
I develop a general formal theory of groundedness and
explain how the well-founded sets, Cantor's extended number-sequence and Kripke's concepts of semantic groundedness are all instances of the general concept, and how the general framework illuminates these cases.
Then, I develop a new approach to a grounded theory of proper classes.
However, the general concept of groundedness does not account for the philosophical significance of its paradigm instances.
Instead, I argue, the philosophical content of the cumulative hierarchy of sets
is best understood in terms of a primitive notion of ontological priority.
Then, I develop an analogous account of Kripke's models.
I show that they exemplify the in-virtue-of relation much discussed in contemporary metaphysics, and thus are philosophically significant.
I defend my proposal against a challenge from Kripke's “ghost of the hierarchy”.