Modern mainstream economists distinguish themselves from both their predecessors and also the current heterodox traditions by their insistence on everywhere employing methods of mathematical deductivist modelling. The modern economics academy is dominated by a mainstream tradition the essence is an insistence on mathematical-deductive modelling. As an intellectual project modern mainstream economics is not in a healthy state. A first notable feature of the modern discipline is that at any point in time many authors seem incapable of avoiding inconsistent accounts of the nature of their project. A second feature of equilibrium theorising in economics is that there are various competing conceptions of equilibrium with the range of notions apparently resistant to successful systematisation, despite the best efforts of some. In truth, modern economics supports two broad sets of traditions, the mainstream project and the heterodox alternatives. The author has illustrated this theme in the context of equilibrium analysis. However the true ontological nature of the differences is rarely explored.