Things could have been different, but could it also have been different what things there are? It is natural to think so, since I could have failed to be born, and it is natural to think that I would then not have been anything. But what about entities like propositions, properties and relations? Had I not been anything, would there have been the property of being me? In this thesis, I formally develop and assess views according to which it is both contingent what individuals there are and contingent what propositions, properties and relations there are. I end up rejecting these views, and conclude that even if it is contingent what individuals there are, it is necessary what propositions, properties and relations there are. Call the view that it is contingent what individuals there are first-order contingentism, and the view that it is contingent what propositions, properties and relations there are higher-order contingentism. I bring together the three major contributions to the literature on higher-order contingentism, which have been developed largely independently of each other, by Kit Fine, Robert Stalnaker, and Timothy Williamson. I show that a version of Stalnaker's approach to higher-order contingentism was already explored in much more technical detail by Fine, and that it stands up well to the major challenges against higher-order contingentism posed by Williamson. I further show that once a mistake in Stalnaker's development is corrected, each of his models of contingently existing propositions corresponds to the propositional fragment of one of Fine's more general models of contingently existing propositions, properties and relations, and vice versa. I also show that Stalnaker's theory of contingently existing propositions is in tension with his own theory of counterfactuals, but not with one of the main competing theories, proposed by David Lewis. Finally, I connect higher-order contingentism to expressive power arguments against first-order contingentism. I argue that there are intelligible distinctions we draw with talk about "possible things", such as the claim that there are uncountably many possible stars. Since first-order contingentists hold that there are no possible stars apart from the actual stars, they face the challenge of paraphrasing such talk. I show that even in an infinitary higher-order modal logic, the claim that there are uncountably many possible stars can only be paraphrased if higher-order contingentism is false. I therefore conclude that even if first-order contingentism is true, higher-order contingentism is false.

Two main questions are addressed in this dissertation, namely: 1. What is the correct higher-order modal theory; 2. What does it take for theories to be equivalent. The whole dissertation consists of an extended argument in defence of the joint truth of two higher-order modal theories, namely, Plantingan Moderate Contingentism, a higher-order necessitist theory advocated by Plantinga (1974) and committed to the contingent being of some individuals, and Williamsonian Thorough Necessitism, a higher-order necessitist theory advocated by Williamson (2013) and committed to the necessary being of every possible individual. The case for the truth of these two theories relies on defences of the following metaphysical theses: i) Thorough Serious Actualism, according to which no things could have been related and yet be nothing, ii) Higher-Order Necessitism, according to which necessarily, every higher-order entity is necessarily something. It is shown that Thorough Serious Actualism and Higher-Order Necessitism are both implicit commitments of very weak logical theories. Prima facie, Plantingan Moderate Contingentism and Williamsonian Thorough Necessitism are jointly inconsistent. The argument for their joint truth thus relies also on showing i) their equivalence, and ii) that the dispute between Plantingans and Williamsonians is merely verbal. The case for i) and ii) relies on the Synonymy Account, an account of theory equivalence developed and defended in the dissertation. According to the account, theories are equivalent just in case they have the same structure of entailments and commitments, and the occupiers of the places in that structure are the same propositions. An immediate consequence of the Synonymy Account is that proponents of synonymous theories are engaged in merely verbal disputes. The Synonymy Account is also applied to the debate between noneists and Quineans, revealing that what is in question in that debate is what are the expressive resources available to describe the world.