Logic already spanned a great range of topics before the birth ofcategorical logic. Some celebrated results achieved in logic duringthe first half of the twentieth century are milestones in the understandingof mathematical relations between syntactic, semantic and algorithmicaspects of the structure of language and reasoning. Logical toolshave been exploited in a variety of applications: from linguisticsto computer science, from methodology of science to specific physicaltheories. The very formulation of questions and answers concerningthe foundations of mathematics relies on such tools. Finally, mathematicallogic has altered the face of philosophy. In view of such outcomes,it is all the more appropriate to consider the impact of categoricalmethods on logic, since they affect the study of proofs and models,by forging a stricter relationship between a theory and its models,and by enlarging the range of possible models beyond the universeof sets in a way that leads to a substantial refinement of the statusascribed to logic itself.
DeVidi, D., Hallett, M., & Clark, P. (2011). Logic, Mathematics, Philosophy: Vintage Enthusiasms- Essays in Honour of John L. Bell. Springer.