Terry and Wolfram's comments are amusing, but are missing the target. As Lakatos argued, any research program have a hard core and protective belts. Terry and Wolfram are talking about protective belts. When we want to define a school of economics, we should detect the hard core. Political opinions and arguments belong to protective belts.
In my last post, I wrote about theoretical framework. I was talking about the hard core of classical and neoclassical economics. Hick's characterization may be too coarse as a definition and we have to add more words in order to get a clear definition of the hard core of the neoclassical economics. It must contain at least two pillars:
(1) a framework of analysis based on agents' optimization and system's equilibrium,
(2) a value theory built on the above framework, i.e. a theory that economic states can be described by the equilibrium point of demand and supply functions.
(1) is more general and characterize the methodology of neoclassical economics but remains too abstract. As a hard core of economics, it needs to contain the second pillar. The prototype of (2) was formed at the time of Jevons and Marshall, but it is better to say that it was Marshall who created the very prototype in the form of crossing point of demand and supply curves. This is what I believe as the rough history of economics in English speaking world. Cases of countries in the European continent may be very different.