Section: Language and Computation
Physicists speak of mesoscopic systems when these contain, say, fifty atoms: too large to be given a microscopic quantum-mechanical description but too small for the classical macroscopic properties to dominate the behavior of the system. Linguistic systems are mesoscopic in the same broad sense: they have thousands of rules and axioms, compared to the handful of axioms and axiom schemes used in most branches of mathematics. Statistical techniques, by their very nature, can yield only approximations for mesoscopic systems. Deductive techniques, though in principle easy to extend to the mesoscopic domain, are in practice also prone to all kinds of bugs, ranging from plain errors of fact (which are hard to avoid once we deal with thousands of axioms) to more subtle, and often systematic, errors and omissions. Students of logic often feel very uncomfortable with the idea that a given system is only 70%, 95%, or even 99.99% correct: after all, isn't a single contradiction or empirically false prediction enough to render a theory invalid? In this course we develop the tools needed to address this question.
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