DELIA GRAFFFARA She philosophized about vagueness — and lived with it too. B Y J A M E S R Y E R S O N • • Tackling a paradox: Fara in 2004. CreditSteve Pyke It applies not just to being a heap but also to being tall. one grain. it remains a heap. or classical logic is flawed (perhaps it is only ever sort of true that something is a heap). was looking for a solution that addressed a common-sense question: If there is a precise point at which a heap becomes a nonheap — and unless you want to abandon natural language . say. Something has gone wrong. a philosopher at Princeton. Others argued that vagueness was a result of semantic indecision: that there are lots of possible things we could mean by “heap. but we don’t know what it is. This is absurd: One grain is not a heap. as it defies easy understanding. Some philosophers argued that vagueness was a form of ignorance: that there is a precise number of grains separating a heap from a nonheap. Delia Graff Fara. or there is no such thing as a heap. which originated with the ancient Greeks. We want to take seriously our talk of hot and cold weather. YOU MIGHT APPROACH IT AS A PUZZLE. Still others. You might approach it as a puzzle. only to end up devising a solution so deep that it would challenge our thinking about language. but we haven’t taken the trouble to specify that meaning. Repeat this process enough times. which experimented with degrees of truth. Either there is a precise number of grains at which point a heap becomes a nonheap.” each of which would establish a precise number of grains for heap-hood. knowledge and the nature of reality. ONLY TO END UP DEVISING A SOLUTION SO DEEP THAT IT WOULD CHALLENGE OUR THINKING ABOUT LANGUAGE. looking to avoid a sharp distinction between heaps and nonheaps. When Fara began working on this paradox as a graduate student at the Massachusetts Institute of Technology in the 1990s. But Fara. herself a skilled practitioner of logic and formal semantics. KNOWLEDGE AND THE NATURE OF REALITY. day and night. often in ways that minimized their oddities. Fara was unsatisfied with the solutions on offer. a brainteaser that must have some clever catch. But it reveals itself. or red. By the time of her death from brain cancer in July at 48. but it is not obvious what. philosophers had come to view it as an instance of a larger problem: vagueness. or bald. Which bullet to bite? This paradox. however. had done just that. to be a philosophical problem. or soft — or any other gradient-like property. If you remove a single grain. and you have a heap of sand that contains. is troubling because it is ubiquitous. but the boundaries that distinguish such things can seem blurry to the point of incoherence.The “paradox of the heap” seems at first like a trick. These solutions were advanced with argumentative ingenuity and technical sophistication. Start with a heap of sand. sought to develop nonclassical or “fuzzy” logics. bald and full-haired men. It was also notable for being written by a young woman in a field that skews heavily toward men.” had an answer. But as much as she let misperceptions slide. Fara became interested in the philosophy of race. because the act of considering two comparable heaps accentuates their similarity. it seems there must be — why are we so inclined to think otherwise? Fara’s theory.” She told her husband she hoped to avoid being defined by her race. “Shifting Sands” became an influential and highly cited paper. you would have despaired of an answer. “the boundary can never be where we are looking. what gets to be tall is also shaped by our interests at a given moment. . which she presented in a 2000 paper called “Shifting Sands. If you enter the gym. But had you been presented with the undivided class and asked to say where the tallness boundary was. James Ryerson is a senior staff editor for The Times’s Op-Ed page and the Ivory Tower columnist for the Book Review. was African-American. Because of her appearance. It would have been more blurry boundaries to think about. Her mother. both demographically and in terms of works cited. you will have no trouble declaring one group the tall students and the other the short ones. who died when she was a child. Fara devoted considerable effort to helping women in the profession. was of Irish and Jewish descent. Imagine that a gym teacher has hastily divided a large class of students into two groups according to height.or classical logic. In fact. an area in which philosophy is similarly lopsided. or answered politely that she was “born in Queens. Concerned about such imbalances.” it was an issue she could never fully escape. if more circumspect. but it “shifts around” as our objectives do. As with all such properties. When it came to racial diversity. Tallness is not just a matter of height. She argued that vagueness was an expression of our ever- changing purposes: that there is a precise point at which a heap becomes a nonheap.” No wonder we think it doesn’t exist. Fara was also a champion. not least because it had implications for other areas of philosophy. Fara concluded. She wondered if her ideas about vagueness — about how seemingly independent properties of the world are infused with human interests — might be relevant. Fara was often assumed to be white or queried clumsily about where she was “from. her father. who raised Fara as a single parent in New York. At the end of her life.