By examining many cases of non−causal explanations, Langer classifies them as scientific explanations by constraint, really statistical explanations, dimensional explanations, and purely mathematical explanations. Although he homogenizes these four types of non−causal explanations at the metaphysical level, his theory remains pluralistic in nature. Although his theory is profound, there are some shortcomings: first, the definition of the concept of salience is not clear enough; second, the distinction between causal and non−causal explanations is not clearly understood; third, it has not been addressed whether non−causal explanations can avoid the problems faced by the covering−law model; fourth, the modal metaphysics of its theory is not infallible.

non-causal explanations  /  scientific explanations by constraint  /  really statistical explanations  /  dimensional explanations  /  purely mathematical explanations