Higher-order Metaphysics

A striking feature of the human condition is that we find ourselves surrounded by, and embedded within, a world largely independent of our experiences, desires, and behaviour. Attempts to understand this external world lie at the heart of human inquiry. What is the nature of this external reality, and what kinds of entity does it contain?

The sciences supply some answers, e.g. biologists study organisms; psychologists study the mind; astronomers study celestial bodies; quantum physicists study the very small. Yet each science is essentially partial, concerned with only some aspects of reality. Metaphysics, by contrast, studies reality in maximally general and encompassing terms. It investigates questions that escape any individual science. Is there a fully general classification of what exists, within which each science's entities are found? How do the different sciences combine into a unified account of a single reality? And, perhaps most fundamentally of all, what is it to exist in the first place?

Metaphysics had a turbulent 20th century. Under the influence of the positivists, it was rubbished as meaningless pseudo-science for many years. Under the influence of Quine, Kripke, Lewis, and others, however, it rose to become a thriving discipline in the 20th century's closing decades. Today, metaphysics is once again at the heart of philosophy.

Contemporary metaphysics has been deeply shaped by two doctrines inherited from Quine, a key figure in metaphysics' resurgence. The first Quinean doctrine is about existence: questions about what exists should be formulated using quantifiers, i.e. words like "something" and "there is". The second Quinean doctrine concerns the acceptable forms of quantification. Ordinary English quantifiers are what logicians call first-order quantifiers. If you're told that Tibbles purrs, first-order quantifiers allow you to infer that something purrs. They don't allow you to infer that Tibbles "somethings"-that's just not meaningful English. Yet logical systems have been developed that permit that inference. The quantifiers in these systems are called higher-order quantifiers. The second Quinean doctrine says that these higher-order quantifiers are meaningless. These doctrines together constitute a background framework in which much contemporary metaphysics takes place. The framework transforms metaphysical questions about what exists into questions formulated with first-order quantifiers. Call this first-order metaphysics.

An emerging consensus in philosophy of language and logic rejects the second Quinean doctrine. However, this highly technical and abstract field can appear isolated from more familiar philosophical concerns. As a result, its consequences have yet to be fully appreciated. This Fellowship aims to address that, by developing and applying a new framework of higher-order metaphysics.

Higher-order metaphysics begins with an array of different higher-order quantifiers. The first Quinean doctrine converts them into an array of different notions of existence. That replaces our ordinary conception of reality-i.e. what exists-with a new and fragmented one, different fragments corresponding to different higher-order quantifiers. This Fellowship will first explore the view's foundations, and exactly what this fragmentation involves, then apply it to some traditional metaphysical debates. In the metaphysics of truth, for example, an account of truth that uses higher-order quantifiers dates back to Ramsey-a founding figure of the analytic philosophical tradition-and Prior. When viewed from the perspective of higher-order metaphysics, this Ramsey-Prior theory of truth can be seen to combine the core ideas of the two leading contemporary views of truth: correspondence and deflationism. Higher-order metaphysics thus provides a conciliatory new solution to the debate about these two views: it reveals that the two leading views about the metaphysics of truth are not really in competition

Because this Fellowship is couched at a relatively high level of abstraction, it does not naturally lend itself to non-academic impact. Yet at its core is a neglected, and fascinating, story in the history of the scientific study of language that has not yet been told for a lay audience. The Fellowship's impact beyond academic philosophy will arise from my publicising this story through a variety of public engagement events.

The story traces the evolution of Russell's Paradox, one of the key ideas motivating the anti-Quinean conception of higher-order logic on which this Fellowship focuses. It began life at the end of the 19th century as a devastating blow to Frege's project-which gave rise to modern logic-of explaining knowledge of mathematics in terms of knowledge of logic. By the early 21st century, it had transformed into a constraint on theorising about the meanings of ordinary language, particularly adjectives and verbs. This latter role for Russell's Paradox lies at the heart of this Fellowship's approach to higher-order logic.

Although somewhat abstract, neither this story nor the Paradox itself is essentially more complex than the content of much popular science communication-and a glance at the newspapers, TV schedules, a decent book shop, or even a list of upcoming science-fiction movies is all one needs to see that interest in even quite abstract science is widespread. I know from first-hand experience explaining the Paradox to family, friends, and academics elsewhere in the humanities, that although this logical approach to the study of language is not widely appreciated outside analytical philosophy, the lay public often find it fascinating once introduced to it. I will aim to tell this story about the evolving significance of Russell's Paradox for the general public through presentations at a variety of cultural events-e.g. the University of Birmingham's Arts and Science Festival, the Birmingham branch of the Royal Institute of Philosophy, The Green Man Festival-and also to introduce school-age children to related ideas in a series of workshops for the Philosophy Club at the University of Birmingham School.

This public engagement work has two sorts of potential impact. The first is to raise public awareness of, and interest in, this kind of academic philosophy. Despite being perhaps the dominant form of philosophy in the English-speaking world, analytic philosophy's interests and methods are still not widely appreciated by the non-academic public. This Fellowship's public engagement component will help to address that, by informing people about, and arousing their interest in, a kind of inquiry and collection of topics they wouldn't encounter otherwise.

The second sort of impact will be by provoking people to think philosophically. Careful, systematic argumentation is the foundation of analytic philosophy, "thinking in slow motion" in John Campbell's phrase. But this mode of thought is not often, and not prominently, exhibited in non-academic discourse. This Fellowship's public engagement events will exhibit this philosophical style of thought, and stimulate participants to practice this skill. This is perhaps of even greater value than raising people's awareness of philosophical ideas. Philosophy's argumentative and analytical methodology is a highly transferable skill of value in many areas of life. It centres around careful listening to, and charitable reconstruction of, the views of others, presenting arguments carefully and systematically, taking a variety of types of evidence into account, honing and refining the concepts one uses. By demonstrating these skills in action, the Fellowship's public engagement events will provoke people to reconsider how they think, reason, and assimilate arguments; in other words, to "think philosophically".