I will give an overview of some of my recent work on higher-order contingentism, roughly the view that it is contingent what propositions, properties and relations there are. I first consider closely related versions of this view proposed by Kit Fine and Robert Stalnaker, and show that they provide satisfactory answers to a challenge for higher-order contingentism posed by Timothy Williamson. The formal development of the view due to Kit Fine turns out to be in need of revision, as it appeals to resources not available according to the view itself. I then consider another challenge for higher-order contingentism, namely to account for our seemingly intelligible talk of possible things which according to their metaphysics do not exist; versions of this challenge have been put forward by several authors in different contexts. It can be shown that even in extremely rich languages, the higher-order contingentist views considered here have difficulties meeting this challenge, as there are no plausible ways of paraphrasing the relevant claims concerning merely possible entities.
Wed Dec 7, 10 am till 12 noon: Peter Fritz (Oslo): ‘Logics for Propositional Contingentism’
Robert Stalnaker has recently advocated propositional contingentism, the claim that it is contingent what propositions there are. He has proposed a philosophical theory of contingency in what propositions there are and sketched a possible worlds model theory for it. Such models can be used to interpret two propositional modal languages: one containing an existential propositional quantifier, and one containing an existential propositional operator. I present results which show that the resulting logic containing an existential quantifier is not recursively axiomatizable, and that a natural candidate axiomatization for the resulting logic containing an existential operator is incomplete.
Thu Dec 8, 11 am till 1 pm: Peter Fritz (Oslo): ‘Predication and Existence’
Contingentists, those who think that it is contingent what individuals there are, face the following question: is it possible for relations to relate individuals there could be, but there aren’t? Higher-order contingentists, roughly those who think that it is contingent what propositions, properties and relations there are, face the analogous question for propositions, properties and relations. I argue first that higher-order contingentists should answer both questions positively: relations relate not only what there is, but also what there could be. I then show that higher-order contingentists have ways of talking about relations, properties and propositions which there could not possibly be, namely by constructing them out of relations, properties and propositions there could be. Such possibilities open up a further question: is it possible for relations to relate lower-level relations, properties or propositions there could not possibly be? I argue that higher-order contingentists should also answer this questions positively: relations relate not only what there is and what there could be, but also what there couldn’t be.
All talks in Edgecliffe, The Scores, St Andrews: Room G03