This article summarizes Ockham's interpretation of Aristotle's categories, showing how his account of connotative concepts introduced a revision in the Aristotelian doctrine about the relation between mathematics and physics. The article shows that Ockham's account influenced William of Heytesbury, John Dumbleton, and Nicholas Oresme to re-interpret disciplinary relations and disciplinary boundaries. They did so, however, in ways compatible with other basic principles of Aristotelian philosophy of nature; nevertheless, their modifications of the Aristotelian account of mathematics stimulated later philosophers to construct (...) robust theories of mathematics compatible with modern mathematical physics. (shrink)

The late scholastics, from the fourteenth to the seventeenth centuries, contributed to many fields of knowledge other than philosophy. They developed a method of conceptual analysis that was very productive in those disciplines in which theory is relatively more important than empirical results. That includes mathematics, where the scholastics developed the analysis of continuous motion, which fed into the calculus, and the theory of risk and probability. The method came to the fore especially in the social sciences. In legal theory (...) they developed, for example, the ethical analyses of the conditions of validity of contracts, and natural rights theory. In political theory, they introduced constitutionalism and the thought experiment of a “state of nature”. Their contributions to economics included concepts still regarded as basic, such as demand, capital, labour, and scarcity. Faculty psychology and semiotics are other areas of significance. In such disciplines, later developments rely crucially on scholastic concepts and vocabulary. (shrink)