Kevin Richardson (Duke University), "Derivative Indeterminacy"

Erkenntnis, 2025

By Kevin Richardson

Our concepts are vague: old, tasty, red, book, slippery, solid, cold, man, and so on. The vagueness of our concepts generally does not leap out at us, on an everyday basis, because we often apply vague concepts to determinate cases. Is Larry David, the star of HBO's Curb Your Enthusiasm, bald? Yes. But he did not go bald overnight. He started with a full head of hair. Then he began to lose hairs. At some point, Larry David entered the ranks of bald men. However, there was a point in the middle where it was vague whether Larry David was bald.

Human language is shot through with vagueness. Our language is not precise enough to capture all the situations we run into, and for good reason: perfect precision would make language and thought a nightmare. We do not go around with a precise way to determine who is young or old, who is bald or non-bald, and so on. Such precision is unnecessary and unsuited to the task of coping with everyday life. We need vague language because, well, life is vague.

But what does it mean, exactly, for life to be vague? The standard approach in philosophy has been to take the vagueness of life as a mere metaphor. On linguistic accounts of vagueness, vagueness is a matter of how we use language. The idea is that the term "bald" expresses, not a single meaning, but a cloud of meanings. Each meaning gives us a standard for being bald, where the standard is measured in terms of how many hairs a person must have on their head. The fuzziness of "bald" consists in the fact that some of these meanings will give conflicting standards.

The details vary, but the basic idea is that vagueness is in our concepts, not our reality. In "Derivative Indeterminacy," I argue that this view is mistaken. Our concepts are vague (or indeterminate) because reality itself is vague. This is the ontic view of vagueness. The ontic theory has historically been met with incredulity and suspicion. There are various objections to ontic vagueness, but one objection concerns the overall mysteriousness of ontic vagueness.

We can see ordinary objects – tables, chairs, pencils – using our ordinary perceptual faculties. We can also see that these objects have the ordinary properties – color, shape, size – that they do. When challenged, we can go further and talk about the physical properties of ordinary objects, as understood by the empirical sciences.

In contrast, vague objects and properties are quite mysterious. We can be uncertain about whether something is a table. We can also fail to know whether something is a table. But what is it to detect an indeterminate table, independently of our inability to articulate or know the determinate facts about the existence of tables? Ontic vagueness appears to create more questions than it answers.

In response, I argue that ontic vagueness in fact does exist, even if we have overwhelming reason to believe that reality is fundamentally precise. My claim is that ontic vagueness is derivative in the sense that: whether something is ontically vague will be fully metaphysically explained (or grounded) in fully determinate facts.

Take the putative fact (J) that it is indeterminate whether Jacky is bald. The fact J will depend on a host of determinate facts: namely, that Jacky is bald-by-standard-1 and Jacky is not bald-by-standard-2. I am simplifying quite a bit here. The property of being-bald-by-standard-X stands in for a more complicated property regarding what I call precisificational possibilities. The basic idea is that there are determinate facts associated with being bald that fully make it the case that it is indeterminate whether someone is bald.

So understood, there is nothing especially mysterious about ontic vagueness. Ontic vagueness exists derivatively, as the consequence of what happens when determinate facts clash in a particular way. Here is an analogy. Two people disagree if they make conflicting assertions. We do not regard the existence of disagreement as an ontological dangler because we know that the existence of disagreement is grounded in facts about assertion. Similarly, I claim that ontic vagueness is perfectly acceptable when we think of it as grounded in determinate facts that conflict in some sense. Any mysteries may be attributed to thinking that vagueness is metaphysically fundamental, as being part of the "ground floor" of reality, so to speak.

What is gained by taking indeterminacy to be derivative? I do not say much about this in the recently published paper, but I will take the opportunity to give a broader motivation here. The basic benefit of accepting derivative indeterminacy is that it allows us to do first-order work on indeterminate aspects of reality. Instead of arguing that indeterminacy really is ontic, we can spend more time examining the nature and consequences of ontic indeterminacy.

I have argued in a series of papers (and a book) that we profit from simply taking the indeterminacy of social reality as a given in social theorizing. Social reality looks vague because it is. (The papers: "Social Construction and Indeterminacy" (Analytic Philosophy); "Exclusion and Erasure: Two Types of Ontological Oppression" (Ergo); "The Metaphysics of Gender is (Relatively) Substantial" (Philosophy and Phenomenological Research); "'Just a Little Gay': How Sexual Orientation Comes in Degrees" (Journal of Philosophy, Forthcoming). The book: The End of Binaries: How Gender and Sexuality Come in Degrees (Oxford University Press, Forthcoming).)

I believe similar benefits would (and do!) result from theorizing about moral, mathematical, modal, nomological indeterminacy. As I imagine it, such theorizing would not solely consist in determining whether there is indeterminacy. A much more interesting project would be to elaborate on the consequences (or lack thereof) of indeterminacy in various domains. This is the kind of project that my intervention in "Derivative Indeterminacy" paves the way for.