 Returning now to our non-Hilbertian focus, the earlier formalism which Frege attacked does not divide mathematics into the aforementioned dual categories of the finitary/contentful, and the infinitary/essentially meaningless but, on the contrary, treats all of mathematics in a unitary and homogeneous fashion. From now on I will use ‘formalism’, to refer to the non-Hilbertian positions and will start with an account of the formalist views distilled by Frege from Heine and Thomae and the criticisms he made of them. These criticisms are widely believed now to contain conclusive refutations of the Heine/Thomae approach. But there are a number of post-Fregean views which seem heavily influenced by, or strongly analogous to, formalism. I will go through these in turn: