Next Thursday, November 26, I’ll be at the Munich Center for Mathematical Philosophy to make my case for quadratic entropy (instead of Shannon’s) in formal philosophy of science. Title and abstract below.
Gini vs. Shannon: The case for quadratic entropy in formal philosophy of science
A probabilistic representation of the notion of uncertainty is an important tool in formal philosophy of science and epistemology: it yields theoretical and mathematical connections with the informativeness of a statement, gradational accuracy, evidential support, how a probability distribution diverges from another, the expected informational utility of an experiment, and more besides. Whenever a choice is made for a measure of uncertainty in these contexts, Shannon entropy is standard, but it is by no means the only option available. In fact, I will question the motivation for this predominance, and suggest that it may be due to historical accident more than fully compelling theoretical reasons. The attractive features of Shannon entropy as a representation of epistemic uncertainty may have been oversold or just taken for granted too quickly, while the comparative appeal of at least one competing approach (quadratic entropy) has been largely neglected.