Invariance principles underlie many key theories in modern science. They provide the explanatory and predictive framework necessary for the rigorous study of natural phenomena ranging from the structure of crystals, to magnetism, to relativistic mechanics. Vigo (2008, 2009)introduced a new general notion and principle of invariance from which two parameter-free (ratio and exponential) models were derived to account for human conceptual behavior. Here we introduce a new parameterized exponential “law” based on the same invariance principle. The law accurately predicts the (...) subjective degree of difficulty that humans experience when learning different types of concepts. In addition, it precisely fits the data from a large-scale experiment which examined a total of 84 category structures across 10 category families (R-Squared =.97, p < .0001; r= .98, p < .0001). Moreover, it overcomes seven key challenges that had, hitherto, been grave obstacles for theories of concept learning. (shrink)

Just as Boolean rules define Boolean categories, the Boolean operators define higher-order Boolean categories referred to as modal categories. We examine the similarity order between these categories and the standard category of logical identity (i.e. the modal category defined by the biconditional or equivalence operator). Our goal is 4-fold: first, to introduce a similarity measure for determining this similarity order; second, to show that such a measure is a good predictor of the similarity assessment behaviour observed in our experiment involving (...) key modal categories; third, to argue that as far as the modal categories are concerned, configural similarity assessment may be componential or analytical in nature; and lastly, to draw attention to the intimate interplay that may exist between deductive judgments, similarity assessment and categorisation. (shrink)