BNHPP: Siddharth Muthukrishnan – Grace Under Pressure: Why Vague Models are Fault-Tolerant

A lecture organized by the Boston Network for the history and Philosophy of Physics, sponsored by the The Center for Philosophy and the History of Science and Tufts University. Abstract: Vague terms, like “tall”, “bald”, and “heap”, have unsharp boundaries. What function, if any, does such unsharpness serve? Attempts to answer this question have focused mostly on ordinary language, with some recent focus on specialized languages such as legal language. I look farther afield—to physics. Physics may seem an unlikely place to find vagueness given its reputation for mathematical precision, but I show that it is shot through with vagueness. Specifically, models employed by physics have vaguely specified regimes of validity, and we can see this clearly using the mathematical structure of relations between models. After I bring this into view, I argue that vagueness serves an important function in physics—namely, fault-tolerance, a notion I borrow from engineering. Roughly, a fault-tolerant system is one that continues functioning—or can be modified so as to continue functioning—if only partially, despite encountering faults, which typically arise because operating conditions depart significantly from those the system was intended for. I argue that, in physics models, the characteristic features of vagueness—namely, sorites-susceptibility, borderline cases, and higher-order vagueness—enable the characteristic features of fault-tolerance—namely, robustness, graceful degradation, and error-correctability. I close by sketching how vagueness enables fault-tolerance in ordinary language as well.