:: Article

Unruly Words

Interview by Richard Marshall.


Diana Raffman is the deft philosophical flautist of vagueness. She thinks hard about vague words and their fuzziness, about supervaluationist approaches to the paradoxes, about judgemental hysteresis, about contextualism and why she changed her mind, about borderline cases, about not sacrificing bivalence, about why she thinks blue but not ‘not blue’ has borderline cases, about her multiple range theory, about changing the way philosophers have understood vagueness and about the epistemic theories of Williamson and Sorensen. This one you have to read before drawing a line….

3:AM: What made you become a philosopher? Were you always philosophically inclined or did something happen?

Diane Raffman : As a child I would often ask my mother (a pianist) questions such as: whether she would find it worse to lose her sight or her hearing (answer: sight, surprisingly), whether she would be willing to lose one of her fingers to save the life of a friend (no), whether she would travel in time if given the opportunity (not sure about that one). She had little pa-tience for these speculations, but my father’s best friend was a philosopher, and he indulged them. Actually I’d planned on a career as a flutist, but I had a small stroke shortly after graduating from college and had to stop playing. Philosophy was the only other subject I’d found exciting enough for a life’s work, so after four years of trying to salvage the flute playing, I applied to graduate school and started studying it seriously.

3:AM: You’re a leading philosopher of vagueness, one of the oldest and most intractable of philosophical puzzles. Before getting into your approach to answering the puzzle can you start by giving us an overview of what you take the puzzle to be and why you think it’s a significant problem even for folk outside of philosophy. To some it might seem trivial.

DR: Good question. Vague words are words that have blurred or “fuzzy” boundaries of application: no clear line divides the things to which they apply from the things to which they don’t. ‘Tall’, ‘old’, and ‘loud’ are good examples. There is no clear line between the people who are tall and the people who are not tall, or between people who are old and people who are not. In contrast, people who are precisely 5’9″ tall are clearly divided from people of any other height, and people who are precisely 70 years old are clearly divided from people of any other age. Having blurred boundaries is often said to consist in having borderline cases—that is, cases where it is supposed to be unclear or indeterminate whether the word applies. For example, a height of 5’11” may be a borderline case for ‘tall’ (relative to, say, American men), and an age of 68 may be a borderline case for ‘old’.

Vagueness is philosophically important for many reasons, but perhaps most of all because it seems to be both an essential feature of natural language and an incoherent one. Vagueness is essential because without it, language would be useless. How could we use these ordinary words if, for example, determining whether someone is tall depended on measuring him to the millimeter, or determining whether someone is old depended on knowing her age to the minute? On the other hand, the use of vague words appears to lead to incoherence. To see how, consider a series of ages progressing from an age at which a person is old, say 80, to an age at which a person is middle-aged, hence not old, say 50. Suppose that each age in the series is one minute younger than the one before it. Then it seems we can generate the following argument:
(1) 80 is an old age.
(2) For any age n, if n is old, then n less 1 minute is old.
(3) Therefore 50 is an old age.
Seemingly impeccable reasoning from seeming impeccable premises leads to an absurd conclusion. This argument is an instance of the sorites paradox, and every vague word is supposed to be susceptible to it.

At first blush the paradox may seem to be just a philosophers’ brain teaser, but as Dorothy Edgington observes, it “affects our lives. There’s the ‘manana paradox’: the unwelcome task which needs to be done, but it’s always a matter of indifference whether it’s done today or tomorrow; the dieter’s paradox: I don’t care at all about the difference to my weight one chocolate will make” (1997, 296). Soritical reasoning may also be familiar from debates about abortion rights: since a newborn infant is a person, and a human organism, say, one second younger than a person is also a person, it seems to follow that a conceptus is a person. The existence of the latter argument suggests that the word ‘person’ too is vague. (Of course, the conclusion that a conceptus is a person is not obviously absurd, so it’s a matter of some urgency for defenders of abortion rights to figure out what is wrong with the paradoxical argument.)


3:AM: There are several approaches to the puzzle that you reject. Before looking at your solution can you say why you reject supervaluationist approaches?

DR: Intuitively speaking, the fundamental idea behind supervaluationism (SV) is that a sentence containing a vague term is true just in case it would be true on all acceptable ways of making the term precise. For example, the sentence ‘Ann’s shirt is blue’ is true just in case it would be true on all acceptable ways of drawing sharp boundaries around the class of blue things. Despite its power and elegance as a formal system, SV has several features that I’d prefer to avoid in a theory of vagueness; I’ll mention three. First, plainly two distinct species of truth are operative in SV, one definable in terms of the other.

The former, called ‘super-truth’, is supposed to be ordinary everyday truth. However, ordinary language doesn’t seem to contain anything analogous to super-truth. (A parallel problem arises with respect to borderline cases, where ‘Ann’s shirt is blue’ is said to be neither super-true nor super-false.) Since vagueness is a feature of ordinary language, this is a problem. Second, supervaluationism has the counterintuitive consequence that a disjunction can be (super) true even where neither of its disjuncts is, and a universal generalization can be (super) false even though none of its instances is.

Third, supervaluationism must reject bivalence, viz., the principle that every declarative sentence either is true or is false. Not everyone would regard this as a defect, but all things being equal we should prefer a theory that doesn’t require it.

3:AM: One thing that’s always interesting is why philosophers chose the arguments they do. Did you go hunting for an alternative approach just to see if it could be done or was it that you looked at the standard fare and felt something was missing?

DR: Not exactly either of these. When I first learned about the sorites paradox, it occurred to me that judgmental hysteresis (a certain dynamical pattern in our use of vague words) could help to solve it. Then I looked at the “standard fare” and thought that none of it provided an intuitively plausible solution; so I began to work out a theory in which the no-tion of hysteresis could play a role. My views are always constrained by what seems to me intuitive. Unlike at least some other philosophers, if a view I’m developing forces me to say something unintuitive, I usually go back to the drawing board.

3:AM: You were for a long time the go-to philosopher for the contextualist response to vagueness. What changed?

DR: It’s probably fair to say that I was the first philosopher to develop a contextualist treatment of vagueness in enough detail to establish contextualism as a genuine alternative to the “standard fare”, as you called it. But important previous work had been done especially by Hans Kamp (e.g., 1975, 1981) and Manfred Pinkal (e.g., 1979, 1984), and also by several linguists whose papers appear in the 1983 collection Approaching Vagueness (ed. Balmer and Pinkal).

As for what changed in my own thinking, I decided that I couldn’t plausibly incorporate the psychological aspects of my contextualist view in the semantics of vague words in the way I had originally envisioned. I now take those psychological aspects to be features of the competent use of vague words, as distinct from their semantics strictly speaking. In addition, I came to see that the distinctive variability of application of a vague expression does not result from any sensitivity to context. Although most if not all vague terms are context-sensitive, their context-sensitivity is not essential to their vagueness. Rather, what’s essential is their possession of multiple equally permissible ways of being applied (multiple permissible “ranges of application”). So the multiple range theory is not a contextualist theory of vagueness.

3:AM: Your new book is called Unruly Words – so this is a semantic approach to vagueness isn’t it?

DR: Yes, thoroughly semantic: vagueness is an aspect of the application of a word. One of the most interesting features of vague words is that their use or application is rule-governed only up to a point. Eventually the rules give out, and our applications of vague words are determined arbitrarily by brute psychological mechanisms. For example, in a sorites series like the series for ‘old’ described above, our stopping places are arbitrary. We diverge from each other and vary in our own classifications from one occasion to the next, and the locations of our stopping places are determined mechanically. There is no reason, no justification, for stopping at any particular place in the series; any particular stopping place is arbitrary. As I see it, this determination by brute mechanism is what makes possible the multiplicity of permissible applications that characterizes vague words.

3:AM: One of the key moves you make is to argue that borderline cases should be defined in terms of contraries rather than contradictions. Can you explain this move?

DR: I can give a basic outline. Borderline cases for a vague word like, say, ‘tall’ are things whose satisfaction of ‘tall’ is supposed to be unclear or problematic: if a given height h is bor-derline tall, it is unclear whether h is tall or not. On the standard philosophical view, borderline cases are defined in terms of the opposition between a term and its negation or contradictory: h is neither definitely tall nor definitely not tall, hence the sentence ‘h is tall’ is neither true nor false. Understood in this way, borderline cases are said to be indeterminate with respect to the vague term in question: there is “no fact of the matter” as to whether h is tall. As a result, borderline cases cannot be represented using classical logic and semantics, according to which every height is either (definitely) tall or (definitely) not tall, and every declarative sentence is either true or false. A lot of nonstandard logical and semantic machinery has been introduced to define borderline cases, employing devices like supervaluations, indeterminate truth-values, and degrees of truth.

I think this machinery is unnecessary. On my view, it is a mistake to define borderline cases in terms of an opposition between contradictories. Instead, borderline cases should be defined in terms of the opposition between incompatible terms like ‘tall’ and ‘average’, or ‘tall’ and ‘above average’: a borderline case for ‘tall’ is neither tall nor average but somewhere between the two, or neither tall nor above average but somewhere between the two. In general, and roughly, a borderline case for ‘tall’ is a height that lies between tall and tall* but is neither tall nor tall*, where ‘tall*’ is an incompatible of ‘tall’. Standard logic and semantics then apply straightforwardly: h is not tall—intuitively, h “comes close” to being tall but doesn’t make it all the way—and the sentence ‘h is tall’ is false. One might say that h falls into the “gap” between tall and above average. There is no threat to excluded middle, so no ‘definitely’ operator is required.

Incidentally, most of the criticism of the incompatibilist approach fails to acknowledge the independent, serious (indeed fatal, in my view) difficulties faced by the standard analysis of borderlines; I discuss some of them in chapter 2 of my book.

3:AM: Is this why Grahame Priest’s paraconsistent approaches are of no use to you in this area? Or were you already determined not to move away from classical logic? I suppose I’m interested in how you decided to reject one logical system for another as it kind of raises those interesting ideas about how one rationally revises one’s logic.

DR: I don’t think I was predisposed to stick with classical logic and bivalence. It’s just that I didn’t believe that a non-epistemic theory of vagueness had to sacrifice bivalence, as is widely supposed. My goal was to design a theory that was as simple and as intuitive as possible and that comported as well as possible with our actual use of vague words. I thought that meeting this goal was essential to an adequate account of vagueness as a feature of ordinary natural language. (Many philosophers working on vagueness see their project as largely formal in nature, so their theories look very different from mine.) The view I developed doesn’t require rejecting classical principles; but if an equally plausible theory can be formulated in a non-classical framework, I would take it very seriously.

3:AM: How can this accommodate the usual idea that borderline cases strike us in terms of indeterminacy?

DR: While we don’t yet have enough psycholinguistic data to know for sure, I expect we’ll find that that “usual idea” belongs to philosophers, not to ordinary speakers. If that’s right, there is no obvious need to accommodate it. That said, the multiple range theorist can cite at least two aspects of borderline cases, compatible with classical principles, that can plausibly be regarded as forms of indeterminacy. First, the claim that (e.g.) a borderline tall height is neither tall nor average but somewhere between the two just is a way of saying that the category membership of the height is indeterminate: h lies in the range between tall and average, but no further classification can be made—provided that ‘tall’ and ‘average’ are the only categories available. (The proviso is essential to the constitution of a borderline case; though h may be clearly above average, insofar as it is borderline tall, the category above average is not available.) Second, heights that can competently be classified as borderline are what I call variable: h can also competently be classified as tall and as average, and this variability can be understood as a form of indeterminacy. There is no single correct way to classify a height like h.

Whether or not borderline cases are taken to be indeterminate in any sense, it is in my view a mistake to build reference to a feeling of uncertainty into the analysis of bor-derline cases, as many theorists of vagueness have tried to do.

3:AM: Critics point to surprising consequences to your approach such as that ‘not blue’ may not have borderline cases even though ‘blue’ has. Is that right? Why doesn’t this worry you?

DR: I say a lot about this in the second chapter of Unruly Words; for now I’ll mention four reasons why I’m not worried. First, I think the notion that a term like ‘not blue’ has borderline cases is a philosophers’ invention. I haven’t tested this (I’ll add it to my ‘data to be collected’ list), but I suspect that ordinary speakers would be baffled by the instruction to point out a borderline not-blue item. Second, presumably the critics you have in mind are motivated by the (classical) logical symmetry between ‘blue’ and ‘not-blue’, but why think that logical relationship should be reflected in the analysis of borderlines? ‘Not blue’ has all sorts of linguistically significant properties that ‘blue’ lacks, and vice versa. For starters, ‘not-blue’ doesn’t name a color, doesn’t even name a perceptual category (there is no way that not-blue things look, one might say), so why expect a symmetry with ‘blue’? Third, the extension of ‘not blue’ is vastly larger and more heterogeneous than the extension of ‘blue’; so again, why expect a symmetry? Lastly, unlike contradictories, incompatible predicates like ‘blue’ and ‘green’, ‘tall’ and ‘average’, ‘old’ and ‘middle-aged’ do merit symmetric treatment, so in fact the incompatibilist analysis of borderlines does a better job of providing for a symmetry than does the standard analysis.


[In-Land: Memories of Space: Sara Maher]

3:AM: You argue for a Multiple Range Theory of vagueness. So what are the distinctive features of your theory?

DR: The fundamental idea is that vagueness consists in a word’s possession of multiple equally permissible or competent ways of being applied, for example multiple equally permissible stopping places in a sorites series. I take the multiple competent ways of using a vague term to reflect multiple ranges of application in its semantics. (It’s this multiplicity that “blurs” the boundaries of a vague term.) A range of application is a set of values (types, properties) to whose instantiations the word can competently be applied. For example, a range of application of ‘tall’ is a set of heights, and a range of application of ‘blue’ is a set of colors. A range of application is not a set of objects, such as tall buildings or blue hats; rather it is a set of values or properties that are instantiated by those objects. A set of tall buildings or blue hats is an extension—or, as I call it, a V-extension—of ‘tall’ or ‘blue’. The fundamental idea is that a vague word has multiple ranges of application relative to a given context; and each range of application, relative to that context, may have different V-extensions at different worlds. According to this multiple range semantics of vagueness, a vague word applies to an item relative to one or more of its ranges of application. The sorites paradox is solved by the fact that every range of application of ‘blue’ has a last member (a last hue). Crucially, however, that last member is simply a permissible stopping point, not a sharp boundary.

3:AM: Doesn’t this approach change the way we’re to understand vagueness? Doesn’t this approach say that vagueness isn’t to be understood in terms of borderlines or bivalence?

DR: It certainly changes the way philosophers have understood vagueness. But actually it preserves, and explains, what is perhaps the most basic intuitive conception of vagueness as possession of blurred boundaries. The philosophical disputes can be seen as disagreements about what unclear boundaries are. Also, my approach preserves the intuition that vague words are tolerant, rather than jettisoning it as some other theorists are forced to do. (On the multiple range theory, tolerance is reconceived in certain ways but retains its most distinctive features; see UW, chapter 5.)

3:AM: Doesn’t it solve the sorites and in general work only by abandoning classical logic because you deny that its possible for there to be a single classical evaluation made in vague uses of language?

DR: Certainly I am calling attention to a new form of variability or multiplicity in the meaning (reference) of a vague word, so it won’t be found in any previous classical approaches. But it doesn’t follow that such a multiplicity cannot figure in a classical semantics. (The term ‘classical semantics’ is surely open-textured in Waismann’s sense.) More importantly, no adequate semantics for natural language, classical or otherwise, can assign a single extension (truth-value) to each predicate (sentence). Just for example, any adequate semantics must accommodate the fact that a single sentence may take different truth values relative to different contexts (e.g., ‘Nancy is tall’ may be true relative to jockeys but not relative to runway models) or relative to different standards or stakes (e.g., if the stakes are low, ‘John knows where his car is parked’ may be true, but not if the stakes are high). If the latter multiplicities of reference don’t make a semantics non-classical, what is the justification for excluding multiple ranges of application?

3:AM: Why wouldn’t an epistemic approach of a Williamson or a Sorensen achieve what you’re wanting?

DR: It might achieve (some of) what I’m wanting—e.g., theoretical simplicity and a clean solution to the sorites paradox—but the price would be prohibitive in a number of respects; let me mention two. First, even epistemicists admit that the notion that vague expressions have sharp boundaries of application is radically counterintuitive; so a theory that achieves the results in question without resorting to sharp boundaries is preferable. The multiple range theory eschews sharp boundaries, relying solely on the innocuous notion of permissible stopping places (e.g.) in a sorites series. Second, consider what epistemicism says: vague words have unknowable sharp boundaries that are fixed by an unknown (unknowable?) function of their unknowable histories of use. Such a multiplication of mysteries veers too close for my comfort to the claim that sharp boundaries of vague terms are fixed by a divine hand. Part of what I have tried to do in Unruly Words is provide a theory of vagueness that is grounded in commonsense intuition and our actual competent use of vague words. In my view it is crucial to remember that vagueness is a feature of ordinary everyday language.

3:AM: And finally for those of us here at 3:AM are there five books other than yours that you could recommend to take us further into your philosophical world?

DR: I think I have been most influenced by the following books (in addition to many individual articles):
Vagueness: An Investigation into Natural Languages and the Sorites Paradox, by Lynda Burns (Kluwer, 1991)
Vagueness, by Timothy Williamson (Routledge, 1994)
Vagueness in Law, by Timothy Endicott (Oxford University Press, 2000)
Vagueness in Context, by Stewart Shapiro (Oxford University Press, 2007)
Vagueness, Gradability, and Typicality: The Interpretation of Adjectives and Nouns, by Galit W. Sassoon (Brill, 2013)


Ballmer, T. and Pinkal, M. (eds.), 1983. Approaching Vagueness. Amsterdam: North Holland.
Edgington, D., 1997. “Vagueness by Degrees”. In R. Keefe and P. Smith (eds.), Vagueness: A Reader (Cambridge, MA: MIT Press).
Kamp, H., 1975. “Two Theories about Adjectives.” In E. Keenan (ed.), Formal Semantics for Natural Language, pp. 123–155. Cambridge: Cambridge University Press.
Kamp, H., 1981. “The Paradox of the Heap.” In U. Mönnich (ed.), Aspects of Philosophical Logic, pp. 225–277. Dordrecht: Reidel.
Pinkal, M., 1979. “How to refer with vague descriptions”. In: R. Bäuerle, U. Egli, and A. v. Stechow (eds.), Semantics from different points of view. Berlin: Springer, 32-50.
Pinkal, M., 1984. “Consistency and context change: The Sorites paradox”. In F. Landman and F. Veltman (eds.), Frontiers of intensional semantics. Dordrecht: Foris, 325-41.

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First published in 3:AM Magazine: Saturday, February 7th, 2015.