Any kind of distinction between what is and what is not empirical is *itself* a non-empirical object. Moreover, the necessary system of thought whose aim is necessarily truth, is uninferred. Not only that, it is uninferable in the strict sense of inferential sequence. But at epistemic rock bottom, that's really not a problem, due to two factors.
First, the definition of the system, in the nature of the case, epistemically exempts the system itself already, yet the reasons that *are given for that system---logic, general reason, and so on---still provide *some kind of justification on the basis of motives, which are in turn driven by values. The reason this is necessary is because the system already has a set of operating values in its standards of intellectual propriety, And because that propriety itself is made up of universals, that system necessarily predicates universal values.
Second, if you could infer this thought system, it would not be the system as defined, because it would itself be justified as true *only* by means of one or more premises that are even more epistemically basic, which contradicts the original definition of the system as the methodologically basic set of cognitive assumptions. If it's basic, it does not itself need a logical basis.
But the system does need an existential basis in motivation and values to be meaningfully preferred as the necessary means of purposive thinking in the pursuit of universal truth---or anything else for that matter. The system of inference is still operating in that sense, but on top of a set of background universal predications of both the rules of thought and basic values, including the values behind standards of intellectual propriety with regard to such universals---as well as those standards themselves.