Most “real world” reasoning is actually material in the sense developed by Sellars and Brandom. The “materiality” of material inference recalls several things.
Material inference addresses meant realities through the medium of their expression in ordinary language.
The “materiality” of material inference also refers to the fact that it always involves meaning-based judgments about proprieties of inference, not simple mechanical application of formal transformations. These may subsequently be given formal representation, but the starting point is what I want to call a form of ethical judgment, that it is right to make this inference about these things in this situation. This could equally be applied to questions of what really is the case, or of the appropriateness of actions. The “meaning” at issue should itself be understood in terms of other normative material inferences, provisionally held constant while the inference at hand is assessed.
Finally, the “materiality” of material inference also recalls its recursive dependence on previous concrete judgments.