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 numbersequence 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”.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:642061 |
| Date | January 2015 |
| Creators | Kriener, Jönne |
| Publisher | Birkbeck (University of London) |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://bbktheses.da.ulcc.ac.uk/121/ |
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