In this chapter I formulate and analyse the definition of the philosophy of the seventeenth- century Scottish universities in terms of 'Reformed scholasticism'. Scholastic philosophy was still central to university teaching after the Reformation, and the Scottish universities produced a great synthesis of Reformed theology and scholastic philosophy. My main focus is on metaphysics: I argue that the Reformed understanding of the Eucharist as a symbol motivated the choice for the views that accidents essentially inhere in their substances and that matter is essentially extended. These views are central to Reformed metaphysics, and qualify Scottish scholasticism as 'Reformed'. They are also coherent with the tradition of Scotism, to which the Scottish scholastics adhered: I argue that they represent developments of Scotism despite being against Duns Scotus's own views. The analysis provides evidence of an original and lively philosophical tradition, an innovative synthesis of Reformed instances, Scotism and Renaissance scholasticism. It was important on a national level, for it influenced philosophy for the whole seventeenth century, and on an international level, through the Scottish presence in the French Protestant academies. The formulation of Reformed scholasticism is a, so far unrecognised, great achievement of the Scottish universities.