Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...) a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

In this chapter, I make the case for platonic realism, the thesis that there are properties that lack spatial locations. After criticizing the one-over-many argument for realism and Lewis's argument for realism, I endorse a modal argument that derives the existence of platonic properties from considerations involving necessary truth. I then defend this argument from various objections. Finally, I argue that epistemic considerations and considerations of parsimony favor a weak form of platonic realism on which there are platonic properties, but (...) each property could have had an instance, and would have been located in its instances if it had any. (shrink)

Commitment to sparseness amounts to the idea that there is an objective, worldly privileging of certain properties over others that makes the privileged properties suited to play certain roles, and is responsible for their playing such roles. In this chapter I offer a brief, opinionated overview of sparseness. I begin by examining a set of problems that I call “problems of abundance”, which generate canonical motivations for sparseness. I then survey some influential approaches to sparseness and the roles that they (...) attribute to sparse properties, noting that on most approaches sparse properties are deeply connected to inquiry. Finally I consider some problems for sparseness, focusing on the purported connections between sparseness and inquiry, particularly in philosophy of science and inquiry into the social world. (shrink)

Commitment to sparseness amounts to the idea that there is an objective, worldly privileging of certain properties over others that makes the privileged properties suited to play certain roles, and is responsible for their playing such roles. In this chapter I offer a brief, opinionated overview of sparseness. I begin by examining a set of problems that I call “problems of abundance”, which generate canonical motivations for sparseness. I then survey some influential approaches to sparseness and the roles that they (...) attribute to sparse properties, noting that on most approaches sparse properties are deeply connected to inquiry. Finally I consider some problems for sparseness, focusing on the purported connections between sparseness and inquiry, particularly in philosophy of science and inquiry into the social world. (shrink)