I am a PhD candidate in philosophy at NYU.

My dissertation is at the intersection of an area of much recent interest---metaphysics conducted in higher-order logical languages---and an older topic, the vexed debate about Absolute Generality. Absolutists claim that it is possible to quantify in a maximally general way, while Relativists claim that it is not. Many philosophers have found the arguments adduced for Relativism compelling. However, it might seem that there is no consistent way to actually say what the Relativist wants to say. "Quantifying in a maximally general way'', for instance, is often glossed as "quantifying over absolutely everything''. The resulting view, though, is incoherent, as David Lewis taught us: if the Relativist claims it is impossible to quantify over absolutely everything, it seems they would be doing exactly that. 

Is any reasonable version of the Absolute Generality debate bound to be settled in the Absolutist's favor?  My dissertation argues not. Lewis shows the incoherence of one way of precisfying the Relativist slogan "it is impossible to quantify in a maximally general way''; I argue that there are other ways of precisfying the slogan, faithful to the Relativists' motivations, which are coherent. The first chapter ("Introducing Absolute Generality'') introduces the debate, and reviews and criticizes some past ways of trying to precisify the Relativist (and hence Absolutist) position. In the second ("Absolute Generality as a Higher-Order Identity''), I argue that, with the resources of higher-order languages, there are ways of precisfying Relativism and Absolutism which capture the spirits of the views. After laying out a methodology for determining whether a given thesis counts as a faithful version or precisification of Relativism or Absolutism, I then offer novel versions of the views using a higher-order language---versions that I prove to be consistent in the third chapter ("Model Theory for Higher-Order Relativism'').

Having set out how I think we should understand Relativism, I turn in the fourth and fifth chapters to seeing whether it is a view we can live with. Much theorizing in metaphysics and mathematics seems to presuppose that our quantifiers are absolutely general in a way that Relativism calls into question. (When we say everything is self-identical, it certainly seems we aim for maximum generality.) The fourth and fifth chapters are case studies of how we can theorize without using absolutely general quantifiers. The fourth chapter ("Set Theory without Quantifiers'') gives a reconstruction of set theory without the use of absolutely general quantification. The fifth chapter ("Quantification and Domains'') does the same with the theory of quantifiers themselves.  Frege famously treated quantifiers as, roughly, certain properties of properties: the existential quantifier is the property of properties P such that a property F has P just when at least one thing is F. This chapter addresses offers answers to questions like "which properties of properties are quantifiers?'' and "what is it to be a domain of quantification?''.