What Machine Learning Tells Us About the Mathematical Structure of Concepts

This is arguably one of the fundamental questions in philosophy, with nearly as many answers as there are philosophers. Aristotle's Categories, Locke's compositional theory of ideas, Kant's transcendental logic, Hegel's concrete universals, Cassirer's Funktionsbegriff, and Wittgenstein's discussion of family resemblance are just a few notable examples of philosophical theories on concepts. Since the last century, philosophical inquiries into concepts have been further accelerated and enriched through interaction with cognitive science, which added an empirical dimension to the discussion. Various models of concepts, such as prototype theory, exemplar theory, and the so-called theorytheory, have been proposed, oftentimes in opposition to or drawing inspiration from existing philosophical theories, and brought to empirical scrutiny (Margolis and Laurence, 1999; Murphy, 2004).