Warmbrod on logical constants

I finished reading the article "Logical Constants" by Ken Warmbrod and what follows is a rough bunch of reflections on it. In the article he gives an analysis of the notion of logicality. He distinguishes two sorts of logicality: core and extended. Core logicality is the primary notion that we are after with logical studies and extended logicality is the cluster of notions that logicians also study but do not fall properly within the scope of core logicality. Core logicality is supposed to minim